Practice final examination.

Solution set for the practice final examination.\

Solution set for the midterm.

Practice Midterm in problem 1 c) note change.<\ /A>

Solution set for the practice midterm.

Homework due October 7: p.A59 2,4,6,8,10,12,14,16,20,22,2426,28,30,32,34,38

Homework due October 14: p.645 2,4,8,10,14,22 p. 653 2,4,6,8 p.659 2,4,6,10,16 p. 668 2,4,16,20,56 p.674 54 p.787 2,6(a),8,12,26,30,34

Homework due October 21:(12.2) p.795 4,6,8,12,14,18,24 (12.3) p.802 2,4,6,12,30,42,48 (12.4) p.809 2,4,16,24,26.

Homework due October 28: p.818 (12.5) 2,4,6,10,20,26,32 p.820 (12.5) 60,62 p.825 (12.6) 4,8,10,14

Homework due November 4: (12.7) p.831 4,8,10,12 (13.1) p.842 2,4,8,12,14,18,30

Homework due November 11: (13.2) p.848 4,6,10,14,24,26,28 (13.3) p.855 2,4 (14.1) p.884 2,6,8,10,22,26,30, 58,60 (14.2) p. 894 4,6,8,14,28.

Homework due November 18:(14.3) 6,12,16,22,56,60 (14.4) p.916 2,4,8,12,14 (14.5) p.924 2,4,6,8,12,26,28,30

Homework due November 22-25: (14.6) p.936 8,10,12,16,22,28 (14.7) p.947 2,6,8,12

Homework due December 2: (14.8) p.956 4,6,10,12,18, p.963 60. (15.1) p.974 2,4,6,12

Syllabus for Math 21C

Syllabus for Math 21C. The parenthetic indicators are to the text Calculus (Early Transcendentals) Fourth Edition by James Stuart. The course will cover the following topics:

The geometry of vectors, functions of vectors and vector valued functions. Partial derivatives. Maximal and minima. Multiple integrals.

The following list is tentative since the fourth edition of Stuartís calculus book has some major differences from the third and we had very little time to study its organization. The point of the syllabus is to give the student an idea of the scope of the course. It is not intended to replace the actual course itself.

1. Complex numbers. De Moivre's formula (Appendix G). Parametrized curves (10.1),tangents areas (10.2) and arc length (10.3),

2. Surface area (10.3). Polar coordinates (10.4). Areas and lengths in polar coordinates (10.5). Three dimensional coordinate systems (12.1).

3. Vectors (12.2): Dot product (12.3 and cross product (12.4). Study of lines and planes using vectors (12.5).

4. Graphical description of level sets (12.6). Cylindrical and spherical coordinates (12.7). Vector functions and space curves (13.1).

5. Arc length and curvature (13.2). Functions of several variables (14.1). Continuity of functions of 2 and 3 variables (14.2).

6. Partial derivatives (14.3): Tangent planes and differentials (14.4), the chain rule and implicit differentiation (14.5).

7. Directional derivatives and the gradient vector (14.6). Maxima and minima (14.7). Lagrange multipliers (14.8).

8. Double integrals over rectangles (15.1). Interated integrals (15.2). More general double integrals (15.3).

9. Double integrals in polar coordinates (15.4). Surface area (15.6). Triple integrals (15.7).