1. Sequence and infinite series
2. Integral test
3. Comparison test
4. Absolute convergence, ratio and root tests
5. Alternating series and conditional convergence
6. Power series and Taylor series
Partial derivatives
1. Limits and continuity in higher dimensions
2. Partial derivatives
3. Chain rule
4. Directional derivatives and gradient
5. Extreme values and saddle points
6. Lagrange multipliers
Multiple integrals
1. Double integrals
2. Area by double integration
3. Double integrals in polar form
4. Triple integrals
5. Cylindrical and spherical coordinates
6. Substitutions in multiple integrals
Integrals and vector fields
1. Line integrals
2. Path independence, conservative fields and potential functions
3. Green's theorem in the plane
4. Surface integrals