# Course Description

## Vector Calculus, MATH 23A

Vectors in n-dimensional Euclidean space. The inner and cross products. The derivative of functions from n-dimensional to m-dimensional Euclidean space is studied as a linear transformation having matrix representation. Paths in 3-dimensions, arc length, vector differential calculus, Taylor's theorem in several variables, extrema of real-valued functions, constrained extrema and Lagrange multipliers, the implicit function theorem, some applications. Students cannot receive credit for this course and MATH 22.

### 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**:

Unit Credit

**UC Davis**:

__General Education__: QL, SE.

__Course Equivalence__: UCD MAT 021C

**UC Irvine**:

__Course Equivalence__: MATH 2D

**UC Los Angeles**:

__Course Equivalence__: Mathematics 32A

Note: Quantitative Reasoning

**UC Merced**:

__Course Equivalence__: UCSC MATH 23A+23B = UCM MATH 023

Units toward degree (see your advisor)

**UC Riverside**:

__Course Equivalence__: MATH 10A

**UC San Diego**:

__General Education__: Revelle - one course towards Math; Warren - Formal skills, may also be used for PofC depending on major/PofC; TMC 1 Mathematics, Advanced Statistics Math GE; Sixth -Structured Reasoning; ERC - meets one course of quantitative formal skills; Muir - as MATH 20B for Math/Natural Sciences GE sequence, Seventh - 1 course towards Alternatives - Quantitative Reasoning; Muir: 1 course in a Natural Sciences theme in "Math and Statistics"

__Course Equivalence__: MATH 20C

**UC San Francisco**:

Unit Credit

**UC Santa Barbara**:

__General Education__: This course will apply to Area C and Quantitative Relationships automatically upon completion

__Course Equivalence__: Likely equivalent to: Math 6A after petition

**UC Santa Cruz**:

__General Education__: MF

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

### Prerequisites

Prerequisite(s): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5.

### Course Fees

There is a fee for the online textbook of approximately $80.

### More About The Course

With a focus on the differential calculus of functions of several variables, Math 23A online is a course which stresses a modern matrix approach to the subject, although a prior knowledge of linear algebra is not required. The online format allows us to probe the historical foundations of the subject and its applications to the physical sciences. The course gives students a greater ability to self-pace their learning, experiment and use technology to further their knowledge and understanding through an interactive and dynamic E-Book and other learning tools. The course offers students an online discussion forum to post questions relating to the video lectures, homework, reading, and course logistics. Students are encouraged to respond to each others questions, and instructors and TA’s monitor these forums, responding to student questions as well. In addition, the teaching staff hold regular online office hours, as well as optional discussion sections.

#### Course Creators

##### Anthony Tromba

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.

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.