MATH 202: CALCULUS III

Math 202: Calculus III

Instructor: John Lind
Office: Krieger 216
Email: jlind@math.jhu.edu
Office hours: Friday 1.30--3.30

Tutorial Sections

For 10-10.50 lecture:
1 Ma T 1:30-2:20 Krieger 308
2 Ma T 3-3:50 Shaffer 302
3 Karami Th 4:30-5:20 Krieger 309
4 Moini Th 1:30-2:20 Krieger 308
5 Paschke T 1:30-2:20 Krieger 300

For 11-11.50 lecture:
6 Mincheva T 4:30-5:20 Krieger 302
7 Paschke Th 1:30-2:20 Hodson 211
8 Zhu Th 3-3:50 Ames 234
9 Zhu Th 4:30-5:20 Krieger 304

Syllabus

Information about PILOT Learning.

Further information about academic support and tutoring.

The homework assignments will be available here at least a week before they are due.
Homework is due on FRIDAYS at the start of lecture.

Midterm I: Solutions (Practice Exam 1, Practice Exam 2, Practice Exam 3)

Midterm II: Solutions (Practice Exam 1, Practice Exam 2 (except problem 5), Practice Exam 3, Practice Exam 4 (except problems 4.2 and 5))

Practice Exams for Final: Practice Exam 1, Practice Exam 2, Practice Exam 3, Practice Exam 4, Practice Exam 5 (except problems 2(b)(c))

Course Schedule:

Topics Sections Homework

Week 1:
Jan 27, 29, 31 Introduction
Three-dimensional Euclidean space
The Inner Product and Lengths of Vectors
Matrices
Determinants and the Cross Product
Cylindrical and Spherical Coordinates § 1.1, 1.2, 1.3, 1.4 Homework 1 (due 2/7):
§ 1.1: 8, 14, 18, 28
§ 1.2: 8, 14, 20, 24, 26, 30
§ 1.3: 2, 12, 22, 28, 34, 38
§ 1.4: 2, 10, 12
Solutions

Week 2:
Feb 3, 5, 7 Multivariable Functions
Linear Functions and Matrices
Limits of Multivariable Functions
§ 2.1, 2.2, 1.5 Homework 2 (due 2/17):
§ 1.5: 10, 21, 22, 24
§ 2.1: 6, 10, 36
§ 2.2: 6, 8, 12, 14, 26
Solutions

Week 3:
Feb 10, 12 The Derivative is the BEST LINEAR APPROXIMATION
The Derivative and the Jacobian Matrix
§ 2.3, 2.4 Homework 3 (due 2/21):
§ 2.3: 2(a)(c), 4(a)(c)(d), 10(a)(d), 16(a)(c), 18, 28
§ 2.4: 8, 18, 24
Solutions

Week 4:
Feb 17, 19, 21 Derivatives: Paths, Velocity and Tangent Vectors
Derivatives: The Chain Rule
The Gradient
Directional Derivatives and Optimization
Iterated Partial Derivatives
§ 2.5, 2.6, 3.1 Homework 4 (due 2/28):
§ 2.4: 6
§ 2.5: 6, 8, 10, 18, 32
§ 2.6: 2(a)(c), 4, 8(a)(b), 22, 24
§ 3.1: 12, 22, 26
Solutions

Week 5:
Feb 24, 26, 28 Taylor Polynomials and Taylor Series
Local Extrema of Scalar-Valued Functions
Constrained Extrema
§ 3.2, 3.3, 3.4 Homework 5 (due 3/10):
§ 3.2: 2, 10
§ 3.3: 6, 14, 28, 30, 44
§ 3.4: 4, 6, 26, 28
Solutions

Week 6:
March 3, 5, 7 Midterm Exam I (March 5)
Constrained Extrema
Extreme Extrema
§ 3.3, 3.4 Homework 6 (due 3/14):
§ 3.4: 24, 38
§ 4.1: 12, 20, 26
§ 4.2: 4, 8, 17(d), 18, 22, 24
§ 4.3: 4, 10, 18
Solutions

Week 7:
March 10, 12, 14 Velocity, Acceleration and Arc-Length
Vector Fields, Divergence and Curl
§ 4.1, 4.2, 4.3, 4.4 Homework 7 (due 3/28)
§ 4.3: 22, 24, 26
§ 4.4: 4, 8, 16, 22, 24, 32, 40
§ 5.1: 2, 12
Solutions

Week 8:
March 24, 26, 28 Double Integrals over Rectangles and Elementary Regions
Changing the Order of Integration
§ 5.1, 5.2, 5.3, 5.4 Homework 8 (due 4/4)
§ 5.2: 2(c)(d), 6, 8
§ 5.3: 4(a)(d)(f), 12
§ 5.4: 2, 4(b)(d), 6(a)(d), 12, 18
§ 5.5: 12, 16, 18
Solutions

Week 9:
March 31
April 2, 4 Triple Integrals
The Change of Variables Theorem
§ 5.5, 6.1, 6.2, 6.3 Homework 9 (due 4/11)
§ 5.5: 14, 22
§ 6.1: 10, 14
§ 6.2: 4, 6, 14, 17, 26, 32
§ 6.3: 10, 16
Solutions

Week 10:
April 7, 9, 11 Applications of Double and Triple Integration
Path Integrals
Line Integrals
Area of Surfaces in R^3
§ 6.3, 7.1, 7.2, 7.3, 7.4 Homework 10 (due 4/18)
§ 6.2: 28, 36
§ 7.1: 8, 12, 18
§ 7.2: 4(a)(b)(d), 6, 8, 18, 20
§ 7.3: 8, 12
Solutions

Week 11:
April 14, 16, 18 Midterm Exam II (April 14)
Integrating Scalar Functions over Surfaces
Integrating Vector Fields over Surfaces

§ 7.4, 7.5, 7.6 Homework 11 (due 4/25)
§ 7.4: 4, 6, 12, 24
§ 7.5: 6, 8, 16, 23, 26
§ 7.6: 2, 6, 14
Solutions

Week 12:
April 21, 23, 25 Orientations of Surfaces and Surface Integrals
Introduction to the Integral Theorems
Stokes' Theorem
Green's Theorem
§ 7.6, 8.1, 8.2 Homework 12 (due 5/2)
§ 8.1: 8, 20, 21, 27
§ 8.2: 6, 13, 18
§ 8.3: 2, 10, 18(a)(c)
§ 8.4: 4, 10(c), 14, 16
Solutions

Week 13:
April 28, 30
May 2 Conservative Vector Fields
Gauss' Theorem
Electricity and Magnetism
Maxwell's Equations
§ 8.2, 8.3, 8.4

FINAL EXAM Wednesday May 7th, 9am -- 12noon in Hodson 110 (**if you have a time conflict with another exam, arrangements will be made in late April)

	Topics	Sections	Homework
Week 1: Jan 27, 29, 31	Introduction Three-dimensional Euclidean space The Inner Product and Lengths of Vectors Matrices Determinants and the Cross Product Cylindrical and Spherical Coordinates	§ 1.1, 1.2, 1.3, 1.4	Homework 1 (due 2/7): § 1.1: 8, 14, 18, 28 § 1.2: 8, 14, 20, 24, 26, 30 § 1.3: 2, 12, 22, 28, 34, 38 § 1.4: 2, 10, 12 Solutions
Week 2: Feb 3, 5, 7	Multivariable Functions Linear Functions and Matrices Limits of Multivariable Functions	§ 2.1, 2.2, 1.5	Homework 2 (due 2/17): § 1.5: 10, 21, 22, 24 § 2.1: 6, 10, 36 § 2.2: 6, 8, 12, 14, 26 Solutions
Week 3: Feb 10, 12	The Derivative is the BEST LINEAR APPROXIMATION The Derivative and the Jacobian Matrix	§ 2.3, 2.4	Homework 3 (due 2/21): § 2.3: 2(a)(c), 4(a)(c)(d), 10(a)(d), 16(a)(c), 18, 28 § 2.4: 8, 18, 24 Solutions
Week 4: Feb 17, 19, 21	Derivatives: Paths, Velocity and Tangent Vectors Derivatives: The Chain Rule The Gradient Directional Derivatives and Optimization Iterated Partial Derivatives	§ 2.5, 2.6, 3.1	Homework 4 (due 2/28): § 2.4: 6 § 2.5: 6, 8, 10, 18, 32 § 2.6: 2(a)(c), 4, 8(a)(b), 22, 24 § 3.1: 12, 22, 26 Solutions
Week 5: Feb 24, 26, 28	Taylor Polynomials and Taylor Series Local Extrema of Scalar-Valued Functions Constrained Extrema	§ 3.2, 3.3, 3.4	Homework 5 (due 3/10): § 3.2: 2, 10 § 3.3: 6, 14, 28, 30, 44 § 3.4: 4, 6, 26, 28 Solutions
Week 6: March 3, 5, 7	Midterm Exam I (March 5) Constrained Extrema Extreme Extrema	§ 3.3, 3.4	Homework 6 (due 3/14): § 3.4: 24, 38 § 4.1: 12, 20, 26 § 4.2: 4, 8, 17(d), 18, 22, 24 § 4.3: 4, 10, 18 Solutions
Week 7: March 10, 12, 14	Velocity, Acceleration and Arc-Length Vector Fields, Divergence and Curl	§ 4.1, 4.2, 4.3, 4.4	Homework 7 (due 3/28) § 4.3: 22, 24, 26 § 4.4: 4, 8, 16, 22, 24, 32, 40 § 5.1: 2, 12 Solutions
Week 8: March 24, 26, 28	Double Integrals over Rectangles and Elementary Regions Changing the Order of Integration	§ 5.1, 5.2, 5.3, 5.4	Homework 8 (due 4/4) § 5.2: 2(c)(d), 6, 8 § 5.3: 4(a)(d)(f), 12 § 5.4: 2, 4(b)(d), 6(a)(d), 12, 18 § 5.5: 12, 16, 18 Solutions
Week 9: March 31 April 2, 4	Triple Integrals The Change of Variables Theorem	§ 5.5, 6.1, 6.2, 6.3	Homework 9 (due 4/11) § 5.5: 14, 22 § 6.1: 10, 14 § 6.2: 4, 6, 14, 17, 26, 32 § 6.3: 10, 16 Solutions
Week 10: April 7, 9, 11	Applications of Double and Triple Integration Path Integrals Line Integrals Area of Surfaces in R^3	§ 6.3, 7.1, 7.2, 7.3, 7.4	Homework 10 (due 4/18) § 6.2: 28, 36 § 7.1: 8, 12, 18 § 7.2: 4(a)(b)(d), 6, 8, 18, 20 § 7.3: 8, 12 Solutions
Week 11: April 14, 16, 18	Midterm Exam II (April 14) Integrating Scalar Functions over Surfaces Integrating Vector Fields over Surfaces	§ 7.4, 7.5, 7.6	Homework 11 (due 4/25) § 7.4: 4, 6, 12, 24 § 7.5: 6, 8, 16, 23, 26 § 7.6: 2, 6, 14 Solutions
Week 12: April 21, 23, 25	Orientations of Surfaces and Surface Integrals Introduction to the Integral Theorems Stokes' Theorem Green's Theorem	§ 7.6, 8.1, 8.2	Homework 12 (due 5/2) § 8.1: 8, 20, 21, 27 § 8.2: 6, 13, 18 § 8.3: 2, 10, 18(a)(c) § 8.4: 4, 10(c), 14, 16 Solutions
Week 13: April 28, 30 May 2	Conservative Vector Fields Gauss' Theorem Electricity and Magnetism Maxwell's Equations	§ 8.2, 8.3, 8.4

FINAL EXAM Wednesday May 7th, 9am -- 12noon in Hodson 110 (**if you have a time conflict with another exam, arrangements will be made in late April)