MA 242 Course Syllabus

Monday

Tuesday

Wednesday

Thursday

Friday

(May 13)

Lecture 1

 Lecture 2

(May 14)

Lecture 3

 Lecture 4 – 1st half

(May 15)

Lecture 4 – 2nd half

Lecture 5

(May 18)

Lecture 6

Lecture 7 – 1st half

(May 19)

Lecture 7 – 2nd half

Lecture 8

(May 20)

Lecture 9

 Lecture 10 – part1

(May 21)

Lecture 10 – 2nd half

Lecture 11

(May 22)

Lecture 12

Lecture 13 – 1st half

(May 25)

HOLIDAY

(May 26)

Lecture 13 – 2nd half

Lecture 14  

(May 27)

Lecture 15

Lecture 16 – 1st half

(May 28)

Lecture 16 – 2nd half

Lecture 17 - review

(May 29)

TEST 1

(2-day window is:

5/28,5/29)

Lecture 18

(June 1)

Lecture 19

Lecture 20 – 1st half

(June 2)

Lecture 20 – 2nd half

Lecture 21

(June 3)

Lecture 22

Lecture 23 – 1st half

(June 4)

Lecture 23 – 2nd half

Lecture 24

(June 5)

Lecture 25

Lecture 26 – 1st half

(June 8)

Lecture 26 – 2nd half

Lecture 27

(June 9)

Lecture 28

Lecture 29 – 1st half

(June 10)

Lecture 29 – 2nd half

Lecture 30 – 1st half

(June 11)

Lecture 30 – 2nd half

Lecture 31 review 

(June 12)

TEST 2

(2-day window is:

6/11,6/12)

Lecture 32

(June 15)

Lecture 33
Lecture 34 – 1st half

(June 16)

Lecture 34 – 2nd half

Lecture 35

(June 17)

Lecture 36

Lecture 37 – 1st half

(June 18)

Lecture 37 – 2nd half

Lecture 38

(June 19)

Lecture 39

Lecture 40 – 1st half

(June 22)

Lecture 40 – 2nd half

Lecture 41

(June 23)

Lecture 42

Lecture 43 – 1st half

(June 24)

Lecture 43 – 2nd half

Lecture 44

(June 25)

Lecture 45

Lecture 46 – 1st half

(June 26)

Lecture 46 – 2nd half

 Lectures 47 –1st half

(June 29)

Lecture 47 – part 3

Lectures 48 Review

(June 30)

TEST 3

(2-day window is:

6/29,6/30)

Lecture 49

(July 1)

Lecture 50

Lecture 51 – 1st half

(July 2)

Lecture 51 – 2nd half

              Lecture 52

(July 3)

HOLIDAY

(July 6)

Lecture 53

Lecture 54 – 1st half

(July 7)

Lecture 54 – 2nd half

Lecture 55

(July 8)

Lecture 56

Lecture 57 – 1st half

(July 9)

Lecture 57 – 2nd half

Lecture 58

(July 10)

Lecture 59

(July 13)

Lecture 60

(July 14)

Lecture 62 Review

(July 15)

TEST 4

(2-day window is:

7/14,7/15)

(July 16)

Lecture 61

Lecture 63 – 1st half

(July 17)

Lecture 63 – 2nd half

Lecture 64

(July 20)

Lecture 65

1st half

(July 21)

Lecture 65

2nd half

(July 22)

Lecture 66

(July 23)

Lecture 67

(July 24)

Lecture 68

(July 27)

Final Exams – Day 1

(July 28)

Final Exams – Day 2

Grades due at 11:59 pm on Thursday 7/30

Lecture #

Chapter

#

Section

#

Topic

1

---

Introduction to the course

1

1

Begin Chapter 1: “Euclidean Geometry in 3-dimensional Space”.

Review Cartesian Coordinates in the Plane; Begin study of Cartesian coordinates in 3-dimensional space.

2

1

2

Begin study of Vectors in two and three dimensions

3

1

2

More on vectors; Positions vector representation of a vector

4

---

Brief discussion of Maple

1

3

Begin study of the dot product of 2 vectors A and B

5

1

3

More on the dot product

1

4

Begin study of the cross product of 2 vectors A and B

6

1

4

More on the cross product

7

1

4

Example: orthogonal decomposition of vector A with respect to vector B

1

5

Equations of Lines and Planes

8

1

5

More on equations of Lines and Planes

9

2

1

Begin Chapter 2: “The Geometry of Curves in Space”

Vector-valued functions, limits and continuity

10

2

1

Differentiating vector-valued functions, rules of differentiation, definite integrals of vector-valued functions

11

2

1

Sketching curves in 3-d using Maple

Anti-derivatives of vector-valued function, parameterized curves

2

Parametrized curves in space, Introduction to the idea of curvature, reparametrizing a curve in terms of arc length,

Initial-value problems, Application: Newton’s second law and motion under gravity

12

2

2

Example of motion under gravity

3

Begin section 3: “Fundamental Quantities Associated with a Curve”,

 Smooth curve, principal tangent vector to a curve, unit tangent vector,  velocity, speed and acceleration of a point particle

13

2

3

Arc length of a curve, arc length reparametrization of a curve, Curvature of a curve

14

2

2

Exercise #23, section 2.2,

3

The curvature of a circle of radius R is K = 1/R, curvature of a curve in terms of an arbitrary parameter

15

2

4

The Unit Normal Vector N,The osculating plane,

Theorem:  Acceleration vector is always parallel to the osculating plane.

The Unit Binormal vector B

16

2

4

The osculating circle of a curve, instantaneous linear and instantaneous centripetal acceleration, simple formulas for the tangential and normal components of acceleration, and for curvature.

17

Review for Test #1

Test #1 on chapters 1 and 2

18

3

1

Begin Chapter 2: “Differential Multivariable Calculus”

Definition and graphical representation; Level curves of f(x,y); Quadric surfaces;

19

3

1

Review level curves of f(x,y); Level surfaces of f(x,y,z),  examples of level surfaces of functions of 3 variables.

20

3

1

Examples of: Ellipsoids, paraboloids, cones, planes and cylinders;

2

Limits of multivariable functions; theorems on limits

21

3

2

Continuity of multivariable functions; theorems on continuity

3

Begin Directional Derivatives of multivariable functions

22

3

3

x-, y- and z-partial derivatives; higher partial derivatives; new notation for partial derivatives

23

3

3

Geometrical interpretation of x- and y-partial derivatives of f(x,y).

Tangent planes to the graph of f(x,y);  Linearization of a function near a point

24

3

4

Differentiability of multivariable functions; examples;

Theorem: a multivariable function is continuous at P if it is differentiable at P. 

25

3

4

Theorem: A multivariable function is differentiable at P if its partial derivatives are continuous at P. 

Examples:  Use the theorem to prove that a function is differentiable at a point.

5

The directional derivative and the Gradient of a function.

Examples.

26

3

5

What does the gradient of the function f tell us about f?

Tangent planes to level surfaces of a function f(x,y,z).

27

3

5

The chain rules for multivariable functions;  Parametrizing functions that are graphs of functions; Implicit differentiation

28

3

6

Optimization of function of two variables:  finding local extreme values of f(x,y);  Examples

29

3

6

The second derivative test;  examples

30

3

6

Global extreme values of f(x,y) on closed and bounded sets

31

Review of chapter 3 for test #2

Test #2 on chapter 3

32

4

1

Begin Chapter 4: “Double and Triple Integrals in Cartesian Coordinates”.  Start with double integrals over rectangles.

33

4

1

Fubini’s Theorem for rectangles.  Examples.

34

4

1

Type I regions.  Fubini’s theorem for Type I regions. Examples.

35

4

1

Type II regions.  Fubini’s theorem for Type II regions. Examples.

36

4

1

Reversing the order of integration; Numerous examples

37

4

2

Applications of double integrals: area; average values; volume between two surfaces; moments and center of mass of plane laminas,

38

4

2

More on applications of double integrals

39

4

3

Triple integrals in Cartesian Coordinates

40

4

3

More on triple integrals:  z-simple, x-simple, and y-simple regions; 

41

4

3

More examples of triple integrals

42

4

3

Applications of triple integrals: Volume; average value; mass and charge density; energy density; moments of inertia

43

5

1

Begin Chapter 5: Double and Triple Integrals in Curvilinear Coordinates.  Begin with double integrals in polar coordinates

44

5

1

Examples of double integrals in polar coordinates

45

5

2

Triple integrals in cylindrical coordinates

46

5

3

Triple integrals in spherical coordinates

47

5

3

More on triple integrals in spherical coordinates; Examples

48

Review of chapters 4 and 5 for test #3

Test #3 on chapters 4 & 5

49

6

1

Begin Chapter 4: “Line and Surface Integrals”.  Start with vector fields in space.  Numerous examples.

50

6

2

Line integrals of functions. 

51

6

2

Solutions to selected exercises in Section 6.2.1 on Line integrals of functions

52

6

3

Line integrals of vector fields.  Work and other examples

53

6

3

The Fundamental Theorem for Line Integrals; Line integrals of vector fields that are independent of path.

54

6

3

Characterizing conservative vector fields.  Finding potential functions for conservative vector fields

55

6

3

More on finding potential functions; Conservation of total energy forNewtonian motion under a conservative force.

4

Parametric surfaces in space

56

6

4

Parametrizing surfaces that are graphs of functions of two variables

57

6

5

Surface integrals; surface area of a parametrized surface;  example:  surface area of a sphere

58

6

5

Surface integrals of functions; examples

59

6

5

Surface integrals of vector fields; examples

60

6

5

More examples of flux integrals

62

Review of chapter 6 for test #4

Test #4 on chapter 6

61

7

1

Begin Chapter 7: “Vector Analysis”.  Start with integral curves of vector fields in space. 

2

Differentiating vector fields:  The divergence and curl.

63

7

2

The concept of “flux density” and its relationship to divergence

64

7

2

Divergence and curl in terms of the “del” operator.  Geometrical interpretation of the divergence and curl of a vector field. A vector field is conservative if and only if its curl is zero.

65

7

2

More on the geometrical interpretation of curl and divergence

3

Green’s theorems for both circulation and flux.  Examples

66

7

4

Stokes’ Theorem.  Examples

67

7

5

The Divergence Theorem of Gauss – begin with review of Green’s theorem for flux.

68

7

6,7

Semester Review

Comprehensive Final Exam