We will use the book `Calculus, early transcendentals' by J. Stewart. The following syllabus is only a rough outline (we may occasionally skip or add some material, or we may move slower or faster depending on how the class goes)
Lec. 1: Sec 10.1: Curves defined by parametric equations.
Lec. 2: Sec 10.2: Tangents and areas for parametric curves.
Lec. 3: Sec 12.1,12.2: Three-dimensional coordinate systems; vectors.
Lec. 5: Sec 12.3: The dot product, projections and components.
Lec. 6: Sec 12.4: The cross product.
Lec. 7: Sec 12.5: Equations of lines and planes.
Lec. 8-9: Sec 13.1-4 vector functions, space curves, arc length
Lec. 10: Sec 14.1: Functions of several variables; level curves.
Lec. 11: Sec 14.2: Limit and continuity.
Lec. 12: Sec 14.3: Partial derivatives.
Lec. 13: Sec 14.4: Tangent planes and linear approximations.
Lec. 14: Sec 14.5: Chain rule (without implicit differentiation).
Lec. 15: Sec 14.6: Directional derivatives and the gradient vector.
Lec. 16: Sec 14.7: Local Maximum and minimum values.
Lec. 17: Sec 14.7: Absolute Maximum and minimum values.
Lec. 18: Sec 14.8: Lagrange multipliers.
Lec. 19: Sec 15.1: Double integrals over rectangles.
Lec. 20: Sec 15.2: Iterated integrals.
Lec. 21: Sec 15.3: Double integrals over general regions.
Lec. 22: Sec 15.4: Double integrals in polar coordinates.
Lec. 23: Sec 15.5/6: Applications of double integrals
Lec. 24: Sec 15.7: Triple integrals.
Lec. 25: Sec.12.7: Cylindrical and spherical coordinates
Lec. 26: Sec. 15.8: Triple integrals in cylindrical and spherical coordinates