MATH 122 – Fall 96

Main topics for the Final Exam

0. Review of techniques of integration, limits, and infinite series • Inverse trigonometric functions. (Sec 8.2)

• Techniques of integrations . (Sec 9.3, 9.4, and 9.5)

• Indeterminate limits and L’Hôpital’s rule. (Sec 8.3 and 8.4)

• Sequences and series. (Sec 11.2 and 11,3)

• Taylor polynomial and series. (Sec 11.4)

1. Algebra of vectors and parametric curves • Operations with vectors in two and three dimensions. (Sec 12.3 and 13.1)

• Dot product, angle between vectors, and distance. (Sec 12.3 and 13.1)

• Cross product and area of parallelograms. (Sec 13.2)

• Equations of lines and planes. (Sec 13.3)

• Parametric curves, velocity and acceleration.(Sec 12.1, 12.4, and 13.4)

2. Differential calculus of functions of several variables. • Visualizing graphs, level curves, and color maps. (Sec 13.6 and 14.2)

• Partial derivatives and chain rules. (Sec 14.3 and 14.7)

• Maxima and minima and the second derivative test. (Sec 14.5 and 14.10)

• Tangential plane and normal vector to a surface; differentials. (Sec 14.4, 14.6, and 14.8)

• Directional derivatives and direction of maximum increase. (Sec 14.8)

• Lagrange multipliers with one constraint. (Sec 14.9)

3. Integral calculus of function of several variables.

• Double integrals and area and volume by double integration. (Sec 15.2 and 15.3)

• Polar coordinates. (Sec 10.2, 10.3, and 15.4)

• Triple integrals. (Sec 15.6)

• Cylindrical and spherical coordinates. (Sec 13.7 and 15.7)

4. Calculus with vector fields.

• Vector fields, divergence and curl. (Sec 16.1)

• Line integrals with respect to arc length. (Sec 12.2, 13.5, and 16.2)

• Line integrals of vector fields and work. (Sec 16.2)