# MATH 1D: CALCULUS

## Foothill College Course Outline of Record

Foothill College Course Outline of Record
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1C.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree & Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Repeatability: Not Repeatable

## Student Learning Outcomes

• Students will solve problems involving applications of multiple integrals and vector calculus.
• Students will develop conceptual understanding of Integration involving functions of multiple variables and theorems and concepts related to vector calculus.
• Students will demonstrate the ability to evaluate multiple integrals, and line and flux integrals.

## Description

Introduction to integration of functions of more than one variable, including double, triple, flux and line integrals. Additional topics include polar, cylindrical and spherical coordinates, parameterization, vector fields, path-independence, divergence and curl.

## Course Objectives

The student will be able to:
A. Demonstrate an understanding of integration of functions of several variables
B. Demonstrate an understanding of parameterization and vector fields, including equations of planes in vector form and using parametric equations, and computation of arc length
C. Demonstrate an understanding of line integrals
D. Demonstrate an understanding of flux integrals
E. Demonstrate an understanding of the calculus of vector fields, including divergence and curl of a vector field, the divergence theorem, Stokes' theorem, and Green's theorem
F. Use technology, such as graphing calculators and/or computer software, to assist in solving problems involving any of the topics in (A) through (E) above
G. Discuss mathematical problems and write solutions in accurate mathematical language and notation
H. Interpret mathematical solutions

## Course Content

A. Integrating functions of several variables
1. The definite integral of a function of two variables
2. Iterated integrals
3. Triple integrals
4. Double integrals in polar coordinates
5. Integrals in cylindrical and spherical coordinates
6. Change of variables in a multiple integral
7. Applications
a. Area
b. Volume
c. Center of mass
d. Moments of inertia
B. Parameterization and vector fields
1. Parameterized curves
a. Tangent vector
b. Normal vector
c. Binormal vector
2. Parameterized surfaces
a. Planes--in vector form and using parametric equations
b. Non-linear surfaces
3. Motion, velocity, and acceleration
4. Vector fields
a. Conservative
5. The flow of a vector field
6. Arc length
7. Curvature
C. Line integrals
1. Parametric equations
2. The idea of a line integral
3. Computing line integrals over parameterized curves
4. Gradient fields and path-independent fields
5. Path-dependent vector fields and Green's theorem
D. Flux integrals
1. The idea of a flux integral
2. Flux integrals for graphs, cylinders, and spheres
3. Flux integrals over parameterized surfaces
E. Calculus of vector fields
1. The divergence of a vector field
2. The divergence theorem
3. The curl of a vector field
4. Stokes' theorem
5. Green's theorem
F. Use technology, such as graphing calculators and/or computer software, to assist in solving problems involving any of the topics in (A) through (E) above
1. Use appropriate technology to graph vector fields and use the graphs to solve various types of problems involving vector fields, such as line integrals, flow lines, divergence and curl
2. Use appropriate technology to graph parameterized curves and surfaces in both 2- and 3-dimensional space
G. Discuss mathematical problems and write solutions in accurate mathematical language and notation
1. Application problems from other disciplines
2. Proper notation
3. Use appropriate technology to graph parameterized curves and surfaces in both 2- and 3-dimensional space
H. Interpret mathematical solutions
1. Explain the significance of solutions to application problems

Not applicable.

## Special Facilities and/or Equipment

Access to graphing technology, such as a graphing calculator or graphing software.

## Method(s) of Evaluation

A. Written homework
B. Quizzes and tests
C. Comprehensive final examination

## Method(s) of Instruction

A. Lecture
B. Discussion
C. Cooperative learning exercises

## Representative Text(s) and Other Materials

Hughes-Hallet, et al. Calculus: Single and Multivariable, Enhanced eText. 7th ed. John Wiley & Sons, Inc., 2017. ISBN 978-1-119-32049-4
Hughes-Hallett, Deborah. MATH 1D: Foothill College Custom Edition. VitalSource Publishing, 2018. ISBN: 9781119541318 www.vitalsource.com/custom/9781119541318. eTextbook without Wiley Plus; contains Chapters 16-21, with odd-numbered homework answers, index, Ready Reference, and differentiation and integration formulas taken from Calculus: Single and Multivariable 7th ed.

## Types and/or Examples of Required Reading, Writing, and Outside of Class Assignments

A. Homework problems covering subject matter from text and related material ranging from 30-60 problems per week. Students will need to employ critical thinking in order to complete assignments.
B. Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
C. Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems, write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system, such as Mathematica or MATLAB.
D. Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed inside and/or outside of class.

Mathematics