Syllabus for MA 1021-1024 using Varberg, Purcell, and Rigdon

MA 1021 Differential Calculus

(Chapters 2, 3, 4)

1.: Functions, operations on functions, trig functions (2.1-2.3)
2.: Limits (2.4-2.6)
3.: Limits of trig functions, infinite limits, limits at infinity (2.7,2.8)
4.: Continuity (2.9)
5.: Introduction to the derivative (3.1, 3.2)
6.: Techniques of differentiation, including trig functions (3.3, 3.4)
7.: Chain rule (3.5)
8.: Leibniz notation (3.6)
9.: Higher order derivatives, implicit differentiation, related rates (3.7-3.9)
10.: Differentials and the linear approximation (3.10)
11.: Extreme values, first and second derivative tests, concavity (4.1-4.3)
12.: Optimization in one dimension, applications (4.4)
13.: Mean value theorem for derivatives (4.7)

About 8 classes for Chapter 2, 11 classes for Chapter 3, and 6 classes for Chapter 4.
Section 4.6 is optional, but students should know how to obtain properties of functions from their graphs. Section 4.5 (economic applications) is also optional.

(Chapters 5, 6, 7, 8)

1.: Antiderivatives and separable differential equations (5.1, 5.2)
2.: The definite integral (5.3-5.5)
3.: Fundamental theorem of calculus, more properties of the definite integral, aids in evaluating definite integrals (5.6-5.8)
4.: Areas of plane regions, solids of revolution via disks and washers (6.1, 6.2)
5.: Arc length (6.4)
6.: Work, moments, and center of mass (6.5, 6.6)
7.: The natural logarithm, inverse functions, natural exponential function (7.1-7.3)
8.: General exponential and logarithmic functions (7.4)
9.: Exponential growth and decay (7.5)
10.: Inverse trig functions (7.7)
11.: Integration by substitution (8.1, 8.3)
12.: Integration by parts (8.4)

About 8 classes on Chapter 5, 6 classes on Chapter 6, 7 classes on Chapter 7, and 3 classes on Chapter 8.
Sections 6.3 (shells), 7.6 (first order DEs) and 7.8 (hyperbolic functions) are optional.

(Chapters 9, 10, 11, 12)

1.: Indeterminate forms (9.1, 9.2)
2.: Improper integrals (9.3, 9.4)
3.: Sequences (10.1)
4.: Series (10.2-10.5)
5.: Power series, Taylor series (10.6-10.8)
6.: Taylor polynomials (11.1)
7.: Numerical integration (11.2)
8.: Solving equations numerically (11.3)
9.: Polar coordinates, including graphing and calculus (12.6-12.8)
10.: Parametric curves in the plane (13.1)
11.: Vectors in the plane (13.2, 13.3)

About 4 classes on Chapter 9, 10 on Chapter 10, 5 on Chapter 11, 3 on Chapter 12, and 3 on Chapter 13.
Section 11.4 (fixed-point methods) is optional.
Emphasis in Chapter 10 should be on geometric series, power series, and Taylor series, not on convergence tests.

(Chapters 13, 14, 15, and 16)

1.: Vector-valued functions, curvilinear motion, and curvature in the plane (13.4, 13.5)
2.: Vectors in three dimensions, dot and cross products (14.1-14.3)
3.: Curves in three dimensions, velocity, acceleration, and curvature (14.4, 14.5)
4.: Surfaces in three dimensions (14.6)
5.: Cylindrical and spherical coordinates (14.7)
6.: Functions of two or more variables (15.1)
7.: Limits, continuity, partial derivatives (15.2, 15.3)
8.: Differentiability and the tangent plane (15.4)
9.: Directional derivatives and the gradient (15.5)
10.: Chain rule (15.6)
11.: More on tangent planes and the linear approximation (15.7)
12.: Extrema of functions of two variables (15.8)
13.: Double integrals, iterated integrals, double integrals over non-rectangular regions (16.1-16.3)
14.: Double integrals in polar coordinates (16.4)
15.: Appplications of double integrals (16.5)
16.: Surface area (16.6)
17.: Triple integrals (16.7)
18.: Triple integrals in cylindrical and spherical coordinates (16.8)

About 3 classes on Chapter 13, 7 on Chapter 14, 7 on Chapter 15, and 8 on Chapter 16.
Section 15.9 (Lagrange multipliers) is optional.

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Last Updated: May 27, 1999