# Course Description

## Calculus for Science, Engineering, and Mathematics, MATH 19A

The limit of a function, calculating limits, continuity, tangents, velocities, and other instantaneous rates of change. Derivatives, the chain rule, implicit differentiation, higher derivatives. Exponential functions, inverse functions, and their derivatives. The mean value theorem, monotonic functions, concavity, and points of inflection. Applied maximum and minimum problems. Students cannot receive credit for both this course and MATH 11A, or AM 11A, or AM 15A, or ECON 11A.

### Key Information

Credit: 5 quarter units /
3.33 semester units credit

UC Santa Cruz, Mathematics

#### Course Credit:

Upon successful completion, all online courses offered through cross-enrollment provide UC unit credit. Some courses are approved for GE, major preparation and/or, major credit or can be used as a substitute for a course at your campus.If "unit credit" is listed by your campus, consult your department, academic adviser or Student Affairs division to inquire about the petition process for more than unit credit for the course.

**UC Berkeley**:

__General Education__: Fulfills College of Letters and Science Quantitative Reasoning

__Course Equivalence__: Math 1A: Math 19A + Math 19B must be completed for credit

**UC Davis**:

__General Education__: QL, SE, SL.

__Course Equivalence__: UCD MAT 021A

**UC Irvine**:

__General Education__: Vb - Formal Reasoning

__Course Equivalence__: Math 2A

**UC Los Angeles**:

__General Education__: Quantitative Reasoning

__Major Preparation__: Psychobiology, Cognitive Science Majors

__Course Equivalence__: Mathematics 31A

**UC Merced**:

__Course Equivalence__: MATH 021 Calc I Phys Sciences & Eng

Units toward degree (see your advisor)

**UC Riverside**:

__Course Equivalence__: UCR Math 009A

UCSC MATH 19A + 19B = UCR MATH 9A + 9B + 9C

**UC San Diego**:

__General Education__: Revelle one course towards Math; Warren - Formal skills, may also be used for PofC depending on major/PofC; TMC - Clears one TMC MATH/LOGIC GE requirement from the Math, Advanced Statistics area; Sixth -Structured Reasoning; ERC - Formal Skills; Muir - as MATH 20A for Math/Natural Sciences GE sequence, Seventh - 1 course; Muir: 1 course in a Natural Sciences theme in "Math and Statistics"

__Course Equivalence__: MATH 20A

**UC San Francisco**:

Unit Credit

**UC Santa Barbara**:

__General Education__: Area C - Science, Mathematics, and Technology, Quantitative relationships

__Course Equivalence__: Math 3A at UCSB

**UC Santa Cruz**:

__General Education__: MF

__Major Requirement__: Lower-division Problem Solving requirement for Mathematics Majors

### Prerequisites

Prerequisite(s): MATH 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher.

### Course Fees

There is a fee for the customized interactive E-text which includes access to the homework, reading assignments as well as the online quizzes and online versions of the exams.

#### Course Creators

##### Anthony Tromba

Anthony (Tony) Tromba was born and raised in New York where he attended The Brooklyn Technical High School. He completed his undergraduate work in Mathematics at Cornell University and received his Ph.D. in Mathematics from Princeton. His first academic position was as Assistant Professor of Mathematics at Stanford University. He later held the Chair of Analysis at the Ludwig Maximilians Universität in Munich, Germany, and is now a Distinguished Professor of Mathematics at the University of California at Santa Cruz.

He has been a Max Planck research group leader, a member of the technical staff at Bell Labs and the Director of Development of the Mathematical Sciences Research Institute in Berkeley, California. Tony has held visiting professorships at many universities throughout the world, including Universities in Paris, Florence, Moscow, Tokyo, Rio de Janeiro, Beijing, Warsaw, and London, He is the author of nine books including the first Mathematics book in the Scientific American Library series. His Vector Calculus textbook, which appears in six editions and five languages, is used by many of America's leading universities.

Anthony (Tony) Tromba was born and raised in New York where he attended The Brooklyn Technical High School. He completed his undergraduate work in Mathematics at Cornell University and received his Ph.D. in Mathematics from Princeton. His first academic position was as Assistant Professor of Mathematics at Stanford University. He later held the Chair of Analysis at the Ludwig Maximilians ...Anthony (Tony) Tromba was born and raised in New York where he attended The Brooklyn Technical High School. He completed his undergraduate work in Mathematics at Cornell University and received his Ph.D. in Mathematics from Princeton. His first academic position was as Assistant Professor of Mathematics at Stanford University. He later held the Chair of Analysis at the Ludwig Maximilians Universität in Munich, Germany, and is now a Distinguished Professor of Mathematics at the University of California at Santa Cruz.

He has been a Max Planck research group leader, a member of the technical staff at Bell Labs and the Director of Development of the Mathematical Sciences Research Institute in Berkeley, California. Tony has held visiting professorships at many universities throughout the world, including Universities in Paris, Florence, Moscow, Tokyo, Rio de Janeiro, Beijing, Warsaw, and London, He is the author of nine books including the first Mathematics book in the Scientific American Library series. His Vector Calculus textbook, which appears in six editions and five languages, is used by many of America's leading universities.

##### Frank Bauerle

Frank Bäuerle was born and raised in southern Germany. He grew up in Weinsberg, a small town amid castle ruins from the Middle Ages and vineyards that were first cultivated by the Romans when they occupied this land some two thousand years ago. He did his undergraduate work in Mathematics and Computer Science at the Technische Hochschule in Karlsruhe, Germany, after which he received his Ph.D. in Mathematics from The University of California at San Diego. Frank did his research work in Recursion Theory and Complexity Theory, an area lying at the intersection of Applied Logic and Theoretical Computer Science.

Frank Bäuerle was born and raised in southern Germany. He grew up in Weinsberg, a small town amid castle ruins from the Middle Ages and vineyards that were first cultivated by the Romans when they occupied this land some two thousand years ago. He did his undergraduate work in Mathematics and Computer Science at the Technische Hochschule in Karlsruhe, Germany, after which he received his ...Frank Bäuerle was born and raised in southern Germany. He grew up in Weinsberg, a small town amid castle ruins from the Middle Ages and vineyards that were first cultivated by the Romans when they occupied this land some two thousand years ago. He did his undergraduate work in Mathematics and Computer Science at the Technische Hochschule in Karlsruhe, Germany, after which he received his Ph.D. in Mathematics from The University of California at San Diego. Frank did his research work in Recursion Theory and Complexity Theory, an area lying at the intersection of Applied Logic and Theoretical Computer Science.