# Course Description

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

The definite integral and the fundamental theorem of calculus. Areas, volumes. Integration by parts, trigonometric substitution, and partial fractions methods. Improper integrals. Sequences, series, absolute convergence and convergence tests. Power series, Taylor and Maclaurin series.

### 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**:

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

__General Education__: Fulfills College of Letters and Science Quantitative Reasoning

**UC Davis**:

__Course Equivalence__: UCD MAT 021B

__General Education__: QL, SE.

**UC Irvine**:

__Course Equivalence__: Math 2B

__General Education__: Vb - Formal Reasoning

**UC Los Angeles**:

__Course Equivalence__: Mathematics 31B

__General Education__: Quantitative Reasoning

__Major Preparation__: Psychobiology, Cognitive Science Majors

**UC Merced**:

__Course Equivalence__: MATH 022 Calc II Phys Sciences & Eng

**UC Riverside**:

__Course Equivalence__: UCR MATH 9B + 9C

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

**UC San Diego**:

__Course Equivalence__: MATH 20B

__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"

**UC San Francisco**:

Unit Credit

**UC Santa Barbara**:

__Course Equivalence__: Math 3B at UCSB

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

**UC Santa Cruz**:

__General Education__: MF

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

### Prerequisites

Prerequisite(s): MATH 19A or MATH 20A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5 of higher.

### Course Fees

There is a fee of about $80 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. There also may be a fee for online proctoring.

### More About The Course

With a focus on integral calculus and infinite series, Math 19B/Calculus 2 is a standard second calculus course with applications to nearly all quantitative-based courses of study including chemistry, computer engineering, computer science, electrical engineering, information systems management, mathematics, and physics majors.

Whether it’s understanding the concept of area under a graph, volumes of surface areas of three-dimensional solids, calculating definite and indefinite integrals using a variety of techniques or computing the Taylor series of a function, the online format of Calculus 2 allows students 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

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.