# Chapter 7: Certificate Programs

## General Information

Certificate programs are designed to provide intensive background in a narrow area at the graduate level. At approximately one-third of the units required for a master’s degree, the certificate is designed to be completed in a much shorter period of time. These certificate programs are appropriate for students working in industry who wish to update their skills or for those interested in changing their career path.

## Interdisciplinary

### Certificate in Frugal Innovation

Advisor: Dr. Aleksandar Zecevic

Over the past two decades, global trends have been forcing businesses to adapt to growing consumer bases in Africa, Asia, and Latin America, which are in desperate need of low-cost and high-quality solutions to the challenges that they face. The importance of these new “economic realities” is underscored by the fact that emerging markets are expected to exceed 50% of the world’s GDP in 2017 (according to IMF estimates). In order to excel professionally in such an environment, engineers will have to be equipped with the knowledge and skill sets to appropriately define, design, and implement solutions that are not merely a “stripping down” of Western products to meet the rising demand. Industry, particularly in Silicon Valley, is becoming increasingly aware of this fact and has begun to move toward a ‘Triple Bottom Line’ approach to business, which integrates environmental, societal, and financial considerations. The Certificate in Frugal Innovation is designed to give students the ability and the tools to adapt to this new model, and to expand their understanding of the impact that engineering has on society.

This program is suitable for working professionals in a wide variety of engineering disciplines. To enroll, students must have a B.S in Engineering from an accredited institution, and should maintain a GPA of at least 3.0 in order to receive the certificate.

**Program Requirements**

The Certificate in Frugal Innovation entails a minimum of 16 units of course work. It consists of an eight-unit Core, and a set of electives that are organized into two groups. Students are required to take four units from Group A and another four from Group B, as described below.

**Required Core Classes (8 units)**

- ENGR 336 Engineering for the Developing World (2 units)
- ENGR 338 Mobile Applications and Instrumentation for Emerging Markets (2 units)
- ENGR 340 Distributed and Renewable Energy for the Developing World (2 units)
- ENGR 341 Innovation, Design and Spirituality (2 units)

**Elective Group A (4 units)**

- ENGR 273 Sustainable Energy and Ethics (2 units)
- ENGR 304 Building Global Teams (2 units)
- ENGR 342 3D Print Technology and Society (2 units)
- ENGR 349 Special Topics in Frugal Engineering (2 units)

**Elective Group B (4 units)**

- CENG 219 Designing for Sustainable Construction (4 units)
- COEN 389 Energy Efficient Computing (2 units)
- ELEN 280/MECH 287 Introduction to Alternative Energy Systems (2 units)
- ELEN 288/COEN 282 Energy Management Systems (2 units)
- ENGR 302 Managing in the Multicultural Environment (2 units)
- ENGR 334 Energy, Climate Change, and Social Justice (2 units)

### Renewable Energy Certificate

Advisor: Dr. Maryam Khanbaghi

Renewable energy is the fastest-growing sector in California and brings together principles and practices from engineering, environmental science, and economics. Silicon Valley, the home of the world’s largest cluster of renewable energy companies and green investors, offers fertile ground to recruit career changers who wish to move into renewable energy and students who want to take advantage of the tremendous career opportunities.

The main goal of this certificate is to introduce students to the field of renewable energy. The intent is to help equip professionals in Silicon Valley with the knowledge that will help them advance in their present career or enter the renewable energy field. To enroll in this certificate, an applicant should have a B.S. in Engineering from an accredited school and should maintain a grade point average of 3.0. As with most certificates in the Graduate School of Engineering, the requirement is 16 quarter units. Eight of these units are in Power Systems, eight units are in Renewable Energy.

**Required Courses (16 units total)**

**Power Systems (8 units)**

- ELEN 280/MECH 287 Renewable Energy (2 units)
- ELEN 281A Power Systems: Generation and Transmission (2units)
- ELEN 281B Power Systems Distribution (2 units)
- ELEN 285 Introduction to the Smart Grid (2 units)

**Renewable Energy (8 units)**

- ELEN 282 Photovoltaic Devices and Systems (2 units) or ELEN 284 Solar Cell Technologies and Simulation Tools (2 units)
- ELEN/MECH 286 Introduction to Wind Energy Engineering (2 units)
- ELEN 287 Storage Device Systems (2 units)
- ENGR 272 Energy Public Policy (2 units)

## Electrical Engineering Certificates

### Digital System Design

Advisor: Dr. Sara Tehranipoor

This certificate program has a triple purpose: (a) to increase design skills in digital system development, (b) to strengthen fundamental knowledge of computer architecture, digital design and embedded systems; and (c) to introduce the digital system designer to state-of-the-art tools and techniques. The program consists of the courses listed below, totaling 16 units. Any change in the requirements must be approved by the academic advisor.

**Required Courses (6 units)**

- ELEN 501 (Embedded Systems) 2 units
- ELEN 511 Advanced Computer Architecture (2 units)

**Elective Courses (10 units)**

- ELEN 387 VLSI Design I (2 units)
- ELEN 388 VLSI Design II (2 units)
- ELEN 500 Logic Analysis and Synthesis (2 units)
- ELEN 502 Real Time Systems (2 units)
- ELEN 503 Hardware-Software Co-design (2 units)
- ELEN 512 Advanced Computer Architecture II (2 units)
- ELEN 513 Parallel System Architectures (2 units)
- ELEN 530 Hardware Security and Trust (2 units)
- ELEN 608 Design for Testability (2 units)
- ELEN 613 SoC (System-on-Chip) Verification ( 2 units)

### Integrated Circuit Design and Technology

Advisors: Dr. Shoba Krishnan, Dr. Cary Yang, Dr. Mahmudur Rahman

The study of integrated circuits consists of three interconnected areas: Design, Devices and Process Technology. This certificate provides the necessary fundamentals in these areas and advanced concepts and application in integrated circuit design and technology. The program will also introduce the IC designer to state-of-the-art tools and techniques. The program consists of the courses listed below; students are required to take a total of 16 units. Any change in the requirements must be approved by the academic advisor.

**Required Courses (8 units)**

- ELEN 252 Analog Integrated Circuits I (2 units)
- ELEN 261 Fundamentals of Semiconductor Physics (2 units)
- ELEN 270 Introduction to IC Materials (2 units)

**Elective Courses (8 units)**

- ELEN 251 Transistor Models for IC Design (2 units)
- ELEN 253 Analog Integrated Circuit Design (2 units)
- ELEN 254 Advanced Analog Integrated Circuit Design (4 units)
- ELEN 264 Semiconductor Device Theory I ( 2 units)
- ELEN 265 Semiconductor Device Theory II (2 units)
- ELEN 274 Integrated Circuit Fabrication Processes I (2 units
- ELEN 275 Integrated Circuit Fabrication Processes II (2 units)
- ELEN 351 RF Integrated Circuit Design (2 units)
- ELEN 352 Mixed Signal IC Design for Data Communications (2 units)
- ELEN 353 DC to DC Power Conversion (2 units)
- ELEN 388 VLSI Design II (2 units)

### Digital Signal Processing and Machine Learning

Advisors: Dr. Tokunbo Ogunfunmi, Dr. Sally Wood

This certificate program provides a basic understanding of digital signal processing theory, machine learning and modern implementation methods, as well as advanced knowledge of at least one specific application area. Digital signal processing and machine learning have become important across many areas of engineering, and this certificate prepares students for traditional or novel applications.

**Required Courses (11 units minimum)**

- ELEN 233 Digital Signal Processing I (2 units)
- ELEN 520 and ELEN 520L Introduction to Machine Learning (3 units)
- At least one course from: AMTH 210 Probability I or AMTH 245 Linear Algebra I or AMTH 370 Optimization Techniques (2 units)
- At least one course from: ELEN 233 Digital Signal Processing System Development (4 units) or ELEN 226 Machine Learning and Signal Processing Using FPGAs (2 units) or ELEN 234 Digital Signal Processing II ( 2 units)
- At least one course from: ELEN 421 Speech Processing I or ELEN 640 Digital Image Processing I (2 units) Note: ELEN 233E Digital Signal Processing I, II (4 units) is equivalent to both ELEN 233 and ELEN 234.

**Elective Courses (Additional courses to make a total of 16 units) selected from the list below:**

- AMTH 308 Theory of Wavelets (2 units) or AMTH 358 Fourier Transforms (2 units)
- ELEN 241 Introduction to Communications (2 units)
- ELEN 243 Digital Communications Systems (2 units)
- ELEN 244 Information Theory (2 units)
- ELEN 247 Communication Systems Modeling Using Simulink I (2 units)
- ELEN 334 Introduction to Statistical Signal Processing (2 units)
- ELEN 422 Speech Coding II (2 units)
- ELEN 431 Adaptive Signal Processing I (2 units)
- ELEN 521 and 521L Deep Learning (3 units)
- ELEN 643 Digital Image Processing II (2 units)
- ELEN 644 Computer Vision I (2 units) or ELEN 645 Computer Vision II (2 units)

### Digital Signal Processing Theory

Advisors: Dr. Tokunbo Ogunfunmi, Dr. Sally Wood

This certificate program provides a firm theoretical grounding in fundamentals of digital signal processing (DSP) technology and its applications. It is appropriate for engineers involved with any application of DSP who want a better working knowledge of DSP theory and its applications. A novel feature of the program is a hands-on DSP hardware/software development laboratory course in which students design and build systems for various applications using contemporary DSP hardware and development software.

**Required Courses (8 units)**

- AMTH 308 Theory of Wavelets (2 units) or AMTH 358 Fourier Transforms (2 units)
- ELEN 233E or ELEN 233 and 234 Digital Signal Processing I, II (4 units)
- ELEN 334 Introduction to Statistical Signal Processing (2 units)

**Elective Courses (8 units)**

- ELEN 223 Digital Signal Processing System Development (4 units)
- ELEN 226 Machine Learning and Signal Processing Using FPGAs (2 units)
- ELEN 235 Estimation I (2 units)
- ELEN 241 Introduction to Communications (2 units)
- ELEN 244 Information Theory (2 units)
- ELEN 336 Detection (2 units)
- ELEN 431 Adaptive Signal Processing I (2 units)
- ELEN 640 Digital Image Processing I (2 units)
- ELEN 641 Image and Video Compression (2 units)
- ELEN 643 Digital Image Processing II (2 units

### Fundamentals of Electrical and Computer Engineering

Advisor: Dr. Shoba Krishnan

This certificate has been designed for those individuals who have significant work experience in some area of electrical and computer engineering and wish to take graduate-level courses but may lack some prerequisite knowledge because they have not earned a BS degree in electrical and/or computer engineering. This one-year program consists of 16 to 28 units, depending on the background of the individual student, and covers electrical and computer engineering core areas. Units from courses at or above the 200 level may be credited toward an MSEE degree after successful completion of the certificate.

The specific required courses for a certificate are selected with the help of the program advisor according to the student’s background.

- ELEN 21 Introduction to Logic Design (5 units)
- ELEN 50 Electric Circuits I (5 units)
- ELEN 100 Electric Circuits II (5 units)
- ELEN 104 Electromagnetics I (5 units)
- ELEN 110 Linear Systems (5 units) or ELEN 210 (2 units)
- ELEN 115 Electronic Circuits I (5 units) or ELEN 250 (2 units)
- ELEN 120 Mircoprocessor System Design ( 5 units)

### RF and Applied Electromagnetics

Advisors: Dr. Timothy Healy, Dr. Kurt Schab

The purpose of this certificate is to meet the increasing need for the knowledge in microwave, antenna and RF integrated circuits in existing electronic products. This program is offered for students who have a B.S. in Electrical Engineering. Students are expected to have knowledge of multivariate calculus and preferably partial differential equations and they must ensure that they have prerequisites for the courses in their program.

The curriculum consists of 16 units: two required courses (4 units) and 12 units of elective courses listed below:

**Required Courses (4 units)**

- ELEN 201 Electromagnetic Field Theory I (2 units)
- ELEN 701 Microwave System Architecture (2 units)

**Elective Courses (12 units)**

- ELEN 202 Computational Electromagnetics (2 units)
- ELEN 203 Bio-Electromagnetics (2 units)
- ELEN 204 Magnetic Circuits for Electric and Autonomous Vehicles (2 units)
- ELEN 351 RF Integrated Circuit Design or ELEN 354 Advanced RFIC Design (2 units each)
- ELEN 624 Signal Integrity in IC and PCB Systems (2 units)
- ELEN 706 Microwave Circuit Analysis and Design (2 units) (Passive Component)
- ELEN 711 Active Microwave Devices I or ELEN 712 Active Microwave Devices II (2 units each) (Active Components)
- ELEN 715 Antennas I or ELEN 716 Antennas II (2 units each)
- ELEN 726 Microwave Measurements, Theory and Tech (3 units) (Laboratory Oriented)

Substitutions for these courses are only possible with the approval of the certificate advisor and the chair.

## MECHANICAL ENGINEERING

### Controls

The Controls Certificate is intended for working engineers in mechanical and closely related fields of engineering. The certificate will provide a foundation in contemporary control theory and methods. The Controls Certificate covers classical and modern control systems and analysis. Specialization in digital control, mechatronics, robotics, or aerospace applications is possible with a suitable choice of electives. Completion of the certificate will allow the student to design and analyze modern control systems.

**Admission**

Applicants must have completed an accredited bachelor’s degree program in mechanical or a closely related field of engineering. They are expected to have prior coursework in undergraduate mathematics. No prior control courses are required.

**Program Requirements**

Students must complete a total of 16 units as described below, with a minimum GPA of 3.0 and a grade of C or better in each course.

**Required Courses (8 units)**

- MECH 217 Introduction to Control (2 units)
- MECH 218 Guidance and Control I (2 units)
- MECH 323 Modern Control Systems I (2 units)
- MECH 324 Modern Control Systems II (2 units)

**Elective Courses (8 units)**

- AMTH 245 Linear Algebra I (2 units)
- AMTH 246 Linear Algebra II (2 units)
- CENG 211 Advanced Strength of Materials (4 units)
- MECH 207 Advanced Mechatronics I (2 units)
- MECH 208 Advanced Mechatronics II (2 units)
- MECH 209 Advanced Mechatronics III (2 units)
- MECH 219 Guidance and Control II (2 units)
- MECH 329 Introduction to Intelligent Control (2 units)
- MECH 355, 356 Adaptive Control I, II (2 units each)
- MECH 429, 430 Optimal Control I, II (2 units each)

### Dynamics and Vibrations

**Objective**

The Dynamics and Vibrations Certificate is intended for working engineers in mechanical and related fields of engineering. The certificate will provide a fundamental and broad background in engineering dynamics. The Dynamics and Vibrations Certificate includes a strong foundational base in dynamics and applications in optimization, robotics, mechatronics, or dynamics of aircraft or spacecraft (depending on the chosen elective courses). Completion of the certificate will allow the student to formulate and solve the complex dynamics problems that arise in such fields as robotics and space flight.

**Admission**

Applicants must have completed an accredited bachelor’s degree program in mechanical or a closely related field of engineering. They are expected to have prior coursework in undergraduate dynamics and mathematics.

**Program Requirements**

Students must complete a total of 16 units as described below, with a minimum GPA of 3.0 and a grade of C or better in each course.

**Required Courses (16 units)**

- MECH 205, 206 Aircraft Flight Dynamics I, II (2 units each)
- MECH 214, 215 Advanced Dynamics I, II (2 units each)
- MECH 305, 306 Advanced Vibrations I, II (2 units each)
- MECH 431, 432 Spacecraft Dynamics I, II (2 units each)

### Materials Engineering

**Objective**

The Materials Engineering Certificate is intended for working engineers in mechanical, materials, or manufacturing engineering. The certificate will provide either an upgrade in materials understanding, or advanced study in a particular aspect of the subject. Completion of the certificate will allow the student to develop a deeper understanding of materials and their applications in design and manufacturing.

**Admission**

Applicants must have completed an accredited bachelor’s degree program in mechanical or a related engineering discipline. They are expected to have prior coursework in basic materials science and strength of materials.

**Program Requirements**

Students must complete 16 units as described below, with a minimum GPA of 3.0 and a grade of C or better in each course.

**Required Courses (12 units)**

- MECH 281 Fracture Mechanics and Fatigue (2 units)
- MECH 330 Atomic Arrangements, Defects, and Mechanical Behavior (2 units)
- MECH 331 Phase Equilibria and Transformations (2 units)
- MECH 332 Electronic Structure and Properties (2 units)
- MECH 333 Experiments in Materials Science (2 units)
- MECH 345 Modern Instrumentation and Control (2 units)

**Elective Courses (4 units)**

- AMTH 210 Introduction to Probability I and AMTH 211 Continuous Probability (2 units each)
- AMTH 217 Design of Scientific Experiments and AMTH 219 Analysis of Scientific Experiments (2 units each)
- CENG 211 Advanced Strength of Materials (4 units)
- ENGR 260 Nanoscale Science and Technology (2 units)
- ENGR 262 Nanomaterials (2 units)
- MECH 273 Designing with Plastic Materials (2 units)
- MECH 274 Processing Plastic Materials (2 units)
- MECH 277 Injection Mold Tool Design (2 units)
- MECH 334 Elasticity (2 units)
- MECH 350 and 351 Composite Materials I and II (2 units each)

### Mechanical Design Analysis

**Objective**

The Mechanical Design Analysis Certificate is intended for working engineers in mechanical or structural engineering. The certificate will provide a succinct upgrade in knowledge and skills that will allow the student to gain a deeper understanding of CAD and FEA principles and practices. Completion of the certificate will allow the student to pursue more advanced design and analysis tasks.

**Admission**

Applicants must have completed an accredited bachelor’s degree program in mechanical, civil, aerospace, or a related field. They are expected to have prior coursework in strength of materials, thermodynamics, fluid mechanics, and mathematics through differential equations.

**Program Requirements**

Students must complete 16 units as described below, with a minimum GPA of 3.0 and a grade of C or better in each course.

**Required Courses (12 units)**

- CENG 205 Finite Element Methods I (2 units)
- CENG 206 Finite Element Methods II (2 units)
- CENG 207 Finite Element Methods III (2 units)
- MECH 325 Computational Geometry for Computer-Aided Design and Manufacture (2 units)
- MECH 334 Elasticity (2 units)
- MECH 415 Optimization in Mechanical Design (2 units)

**Elective Courses (4 units)**

- AMTH 220 Numerical Analysis I (2 units)
- AMTH 221 Numerical Analysis II (2 units)
- AMTH 308 Mathematical Modeling I (2 units)
- AMTH 309 Mathematical Modeling II (2 units)
- AMTH 370 Optimization Techniques I (2 units)
- AMTH 371 Optimization Techniques II (2 units)
- CENG 211 Advanced Strength of Materials (4 units)
- CENG 214 Theory of Elasticity (4 units)
- CENG 222 Advanced Structural Analysis (4 units)
- MECH 268 Computational Fluid Mechanics I (2 units)
- MECH 269 Computational Fluid Mechanics II (2 units)

### Mechatronics Systems Engineering

**Objective**

The Mechatronics Systems Engineering Certificate is intended for working engineers in mechanical engineering and related fields. The certificate program introduces students to the primary technologies, analysis techniques, and implementation methodologies relevant to the detailed design of electro-mechanical devices. Completion of the certificate will allow the student to develop systems that involve the sensing, actuation and control of the physical world. Knowledge such as this is vital to engineers in the modern aerospace, robotics and motion control industries.

**Admission**

Applicants must have completed an accredited bachelor’s degree program in mechanical, aerospace, electrical, engineering physics, or a related field. They are expected to have prior coursework in mathematics through differential equations, introductory linear control theory, and introductory electronics and programming.

**Program Requirements**

Students must complete a total of 16 units as described below, with a minimum GPA of 3.0 and a grade of C or better in each course.

**Required Courses (8 units)**

- MECH 207 Advanced Mechatronics I (3 units)
- MECH 208 Advanced Mechatronics II (3 units)
- MECH 217 Introduction to Control (2 units)

**Elective Courses (8 units)**

- MECH 218 Guidance and Control I (2 units)
- MECH 219 Guidance and Control II (2 units)
- MECH 275A Design for Competitiveness (2 units)
- MECH 310 Advanced Mechatronics IV (2 units)
- MECH 311 Modeling and Control of Telerobotic Systems (4 units)
- MECH 315 Digital Control Systems I (2 units)
- MECH 316 Digital Control Systems II (2 units)
- MECH 323 Modern Control Systems I (2 units)
- MECH 324 Modern Control Systems II (2 units)
- MECH 329 Intelligent Control (2 units)
- MECH 337 Robotics I (2 units)
- MECH 338 Robotics II (2 units)
- MECH 339 Robotics III (2 units)
- MECH 345 Modern Instrumentation (2 units)

An independent study or Capstone project would be suitable as one of the electives. In addition, other courses may serve as electives at the discretion of the program advisor.

### Thermofluids

**Objective**

The Thermofluids Certificate is intended for working engineers in mechanical, chemical, or a closely related field of engineering. The certificate will provide fundamental theoretical and analytic background, as well as exposure to modern topics and applications. Specialization in fluid mechanics, thermodynamics, or heat transfer is possible with suitable choice of electives. Completion of the certificate will allow the student to design heat transfer and fluid solutions for a range of modern applications.

**Admission**

Applicants must have completed an accredited bachelor’s degree program in mechanical or a closely related field of engineering. They are expected to have prior undergraduate coursework in fluid mechanics, thermodynamics and heat transfer.

**Program Requirements**

Students must complete 16 units as described below, with a minimum GPA of 3.0 and a grade of C or better in each course.

**Required Courses (12 units)**

- MECH 228 Equilibrium Thermodynamics (2 units)
- MECH 236 Conduction Heat Transfer (2 units)
- MECH 238 Convective Heat Transfer I (2 units)
- MECH 240 Radiation Heat Transfer (2 units)
- MECH 266 Fundamentals of Fluid Mechanics (2 units)
- MECH 270 Viscous Flow I (2 units)

**Elective Courses (4 units)**

- MECH 202 Mathematical Methods in Mechanical Engineering (4 units)
- MECH 225 Gas Dynamics I (2 units)
- MECH 226 Gas Dynamics II (2 units)
- MECH 230 Statistical Thermodynamics (2 units)
- MECH 239 Convective Heat Transfer II (2 units)
- MECH 241 Radiation Heat Transfer II (2 units)
- MECH 242 Nanoscale Heat Transfer (2 units)
- MECH 268 Computational Fluid Mechanics I (2 units)
- MECH 269 Computational Fluid Mechanics II (2 units)
- MECH 271 Viscous Flow II (2 units)
- MECH 288 Energy Conversion I (2 units)
- MECH 289 Energy Conversion II (2 units)
- MECH 345 Modern Instrumentation and Control (2 units)