WPI Mathematical Sciences Department Worcester Polytechnic Institute


Syllabus for MA 1021-1024 using Edwards and Penney (6th ed. or 7th ed., early transcendentals) published by Prentice-Hall



MA 1021 - Differential Calculus
MA 1022 - Integral Calculus
MA 1023 - Approximation, Series, polar coordinates, and vectors
MA 1024 - Multivariable Calculus



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MA 1021 Differential Calculus

(Chapters 1, 2, 3, 4)

1. Functions, operations on functions, transcendental functions (1.1-1.4)
2. Limit Concepts (1.5-2.2)
3. Limits of trig functions, rigorous definitions, infinite limits, etc. (2.3)
4. Continuity (2.4)
5. Introduction to the derivative (3.1, 3.2)
6. Chain rule and Generalized Power Rule (3.3, 3.4)
7. Optimization in one dimension, applications (3.5, 3.6)
8. Derivatives of standard transcendental functions (3.7, 3.8)
9. Implicit Differentiation, Related Rates (3.9)
10. Newton's Method (3.10)
11. Differentials and linear approximation (4.2)
12. Mean Value Theorem (4.3)
13. Extreme values, first and second derivative tests, concavity, curve sketching (4.4-4.7)

Remarks



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MA 1022 Integral Calculus

(Chapters 5, 6, 7, 8)

1. Antiderivatives (5.2)
2. The definite integral (5.3-5.4)
3. Fundamental theorem of calculus, properties of the definite integral, substitution (5.5-5.7)
4. Areas of plane regions, numerical integration (5.8-5.9)
5. Modelling with Riemann sums (6.1)
6. Volumes (including the "washer method") (6.2)
7. Arc length, Centroids (6.4 and 6.6)
8. The natural logarithm, inverse trig functions (6.7-6.8)
9. Basic techniques of integration: substitution, integration by parts, trigonometric integrals (7.2-7.4)
10. Additional techniques of integration: partial fractions (7.5)
11. Exponential growth and decay (8.1)

Remarks



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MA 1023 Series, approximations, polar coordinates, and vectors

(Chapters 9, 10, 11, and parts of Chapters 4 and 7)

1. Indeterminate forms (4.8-4.9)
2. Improper integrals (7.8)
3. Sequences (10.2)
4. Series (10.3)
5. Taylor polynomials and Taylor series (10.4)
6. Integral test (10.5)
7. Power Series (10.8-10.9)
8. Polar Coordinates (9.2-9.3)
9. Parametric Curves (9.4-9.5)
10. Vectors, dot product, and cross product (11.1-11.3)
11. Lines and planes in space (11.4)
12. Curves in space, motion, curvature, acceleration (11.5-11.6)

Remarks



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MA 1024 Multivariable Calculus

(Chapters 12 and 13)

1. Functions of several variables (12.2)
2. Limits, continuity, partial derivatives (12.3, 12.4)
3. Multivariable optimization (12.5)
4. Linear approximation, differentials (12.6)
5. Chain rule (12.7)
6. Directional derivatives and the gradient (12.8)
7. Critical points (12.10)
8. Double integrals, iterated integrals, double integrals over non-rectangular regions (13.1-13.3)
9. Double integrals in polar coordinates (13.4)
10. Appplications of double integrals (13.5)
11. Triple integrals (13.6)
12. Integration in cylindrical and spherical coordinates (13.7)
13. Surface area (13.8)
14. Change of variables (13.9)

Remarks


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