Syllabus for MA 1021-1024 using Herman and Strang Calculus Volume 1, 2, and 3 (OpenStax)

MA 1021 Differential Calculus

(Calculus Volume 1, Chapters 1, 2, 3, and 4) 

1. Functions, operations on functions, transcendental functions (1.1 , 1.2, 1.3, 1.4, 1.5)
2. Limit Concepts (2.1, 2.2, and 2.3)
3. Rigorous definitions, one-sided limits (2.5, 2.2)
4. Continuity (2.4)
5. Limits involving infinity (4.6)
6. Introduction to the derivative (3.1, 3.2, 3.3, 3.4)
7. Derivatives of trig functions (3.5)
8. Chain rule (3.6)
9. Implicit Differentiation (3.8)
10. Derivatives of inverse functions: logs and inverse trig functions (3.7, 3.9)
11. Related rates (4.1)
12. Differentials and linear approximation (4.2)
13. Extreme values (4.3)
14. Mean value theorem (4.4)
15. First and second derivative tests, concavity, curve sketching (4.5)
16. Applied optimization (4.7)
17. Newton's Method (4.9)

Remarks

About 2 classes for Chapter 1, 4 classes for Chapter 2, 12 classes for Chapter 3 and 7 classes for Chapter 4.
Regarding Section 2.5, the rigorous definition of the limit will not be tested on the common final.
Some faculty may choose to cover sections in an order different from that suggested by the text.
Section 4.8 (L’Hôpital’s Rule and Indeterminate Forms) is optional but will be covered in Calculus III.

MA 1022 Integral Calculus

(Calculus Volume 1, Chapter 4.10,
Calculus Volume 2, Chapters 1, 2, 3, and 4)

1. Antiderivatives (V1 4.10)
2. The definite integral (V2 1.1, 1.2)
3. FToC, substitution for indefinite integrals (V2 1.3, 1.4, 1.5)
4. Areas of plane regions, substitution in definite integrals (V2 2.1, 1.5)
5. Volumes (including the "washer method") (V2 2.2)
6. Arc length, surfaces of revolution (V2 2.4)
7. Moments and centers of mass (V2 2.6)
8. The natural logarithm as an integral (2.7)
9. Exponential growth and decay (V2 2.8)
10. Basic techniques of integration: substitution, integration by parts, trigonometric integrals (V2 1.5, 3.1, 3.2)
11. Additional techniques of integration: partial fractions (V2 3.4)
12. Numerical integration (V2 3.6)

Remarks

About 10 classes for items 1.-4., 6 classes for items 5.-7., 2 classes for items 8.-9., and 7 classes for items 10.-12.
Some faculty may choose to cover sections in an order different from that suggested by the text.
The following sections are optional: (V2 2.3 - Cylindrical Shells), (V2 2.5 - Work), (V2 2.9 -Hyperbolic Functions), (V2 3.3-Trigonometric Substitution) The instructor should cover at least one of the optional sections.

MA 1023 Series, approximations, polar coordinates, and vectors

(Calculus Volume 1, Chapter 4.8,
Calculus Volume 2, Chapters 3.7, 5, and 6,
Calculus Volume 3, Chapters 1, 2, and 3)

1. Indeterminate forms (V1 4.8)
2. Improper integrals (V2 3.7)
3. Sequences (V2 5.1)
4. Series (V2 5.2)
5. Integral test (V2 5.3)
6. Power Series (V2 6.1, 6.2)
7. Taylor polynomials, Taylor series, applications (V2 6.3, 6.4)
8. Parametric Curves (V3 1.1, 1.2)
9. Polar Coordinates (V3 1.3, 1.4)
10. Vectors, dot product, and cross product (V3 2.1, 2.2, 2.3, 2.4)
11. Lines and planes in space (V3 2.5)
12. Curves in space, motion, curvature, acceleration (V3 3.1, 3.2, 3.3, 3.4)

Remarks

About 3 classes on the sections from V1 CH4.5 and V2 CH3.7, 10 classes on V2 CH5 and V2 CH6, 5 classes on V3 CH1, 3 classes on V3 CH2, and 4 classes on V3 CH3.
Some faculty may choose to cover sections in an order different from that suggested by the text.
Sections (V2 5.4, 5.5, 5.6) (Comparison Tests, Absolute Convergence, Alternating Series, Ratio/Root Tests) are optional, but should be part of the syllabus for freshmen in A term and B term.
Note that if sections V2 5.4, 5.5 (comparison tests, alternating series) are not covered, convergence of power series at the endpoints of the interval of convergence should be omitted as well.
Emphasis should be on V2 CH6 geometric series, power series, and Taylor series, not on convergence tests.
Coverage of 3.1 through 3.4 will be a bit rushed, but students know much of this from physics

MA 1024 Multivariable Calculus

(Calculus Volume 3, Chapters 4 and 5)

1. Functions of several variables (4.1)
2. Limits, continuity, partial derivatives (4.2, 4.3)
3. Chain rule (4.5)
4. Directional derivatives and the gradient (4.6)
5. Linear approximation, differentials (4.4)
6. Multivariable optimization (4.7)
7. Double integrals, iterated integrals, double integrals over non-rectangular regions (5.1, 5.2)
8. Area by double integrals (5.1)
9. Double integrals in polar coordinates (5.3)
10. Triple integrals (5.4)
11. Moments and centers of mass (5.6)
12. Integration in cylindrical and spherical coordinates (5.5)
13. Change of variables (5.7)

Remarks

About 11 classes on Chapter 4, 14 classes on Chapter 5.
Sections 4.8 (Lagrange multipliers) and the early sections in Chapter 6.1, 6.2 are optional.