MATH253-105 :       Multivariable Calculus   (1st term 2017/2018)

Lecture   I: Monday 11am--12noon, LSK-200.

Lecture   II: Wednesday 11am--12noon, LSK-200.

Lecture   III: Friday 11am--12noon, LSK-200.

Office Hours: Every Monday, Wednesday, Friday, 4:20pm-5:10pm, LSK 303B.

TA: Narayanan

Course website:

Textbook For MATH253

We are using "APEX Calculus, Version 3.0, Volume 3 (Chapters 9- 13)". Sorry, hard copies cannot be purchased from the bookstore, however, you can buy them from the author's website or from online retailers in CAD Dollar. An electronic copy of this book is also available online at no cost from

Downloads For MATH253

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Updates For MATH253-105

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Sept. 06/17: coordinates systems, planes, lines, distances, spheres

Sept. 08/17: vectors, dot product, projections.

Sept. 11/17: Cross product. Properties of cross product. Applications: area of parallegram formed by two vectors in 2D or 3D, volume of parallelepiped formed by three vectors.

Sept. 13/17: Normal, equation of a plane. distance between a point to the plane. distance between two planes. parallel planes. angle between two planes.

Sept. 15/17: Equation of a line. Curves in $R^3$, tangent vector of a curve, tangent line of a curve at a place (11.1, 11.2). Quadratic curves in $R^2$.

Sept. 18/17: Seven types of quadratic surfaces. Examples. (Please look at Chapter 10.1 for pictures of these surfaces.) Functions of two or three variables.

Sept. 20/17: Functions of two/three variables. Graph. Contour. Limits and Continuity (Keywords: Limit exists if along any path the limit exists and equal)

Sept. 22/17: Continuity. Partial Derivatives. Examples. Notes on Sept. 22

Sept. 25/17: Second order derivatives. interchange of mixed derivatives.

Sept. 27/17: PDEs, Laplace equation, wave equation.

Sept. 29/17: Wave equation. First order PDE. Tangent line. Tangent planes. Linear approximations.

Oct. 02/17: total differentials. Applications; Sensistivity analysis.

Oct. 4/17: Examples of contours. Chain rules of first type. Max or Min of two-variable function on a curve.

Oct. 9/17: Chain rule, Jacobian, Implicit function defferentiation.

Oct. 11/17: Midterm One.

Oct. 13/17: directional derivative, gradient, contour curve, steepest descent.

Oct. 16/17: steepest descent. gradient of three variable functions. tangent plane for implicit surfaces.

Oct. 18/17: Use of gradient to compute the distance to a surface. Taylor expansion, Hessian matrix, local behavior of critical points.

Oct. 20/17: critical points and their types: local min, local max and saddle points. Global min and global max, examples.

Oct. 23/17: example of global max/min. Global max/min with constraints. Lagrange multiplier.

Oct. 25/17: Global max/min with multiple constraints. Lagrange multiplier. Integration of multiple integrals. Notes on Oct. 25 .

Oct. 27/17: Fubini Theorem. Iterated Integrals. Double Integrals of First Type.

Oct. 30/17: Double integrals in Type I and Type II domains. Many examples.

Nov. 1/17: Example Notes on Oct. 25 . Applications of Double Integral.

Nov. 3/17: Reverse order of integrals. Symmetry. Polar Coordinates.

Notes on Riemann sum .

Nov. 6/17: Double integrals using polar coordinates. Example Notes on Nov. 6 .

Nov. 8/17: Examples of double integrals using polar coordinates: area and volume. Mass and center.

Nov. 10/17: Center of mass.

Nov. 13/17: Holiday

Nov. 15/17: Midterm 2

Nov. 17/17: Momentums, inertia

Nov. 20/17: Surface area

Nov. 22/17: Triple integrals. Fubini. Type 0, I, II, III domain

Nov. 24/17: Change of orders in triple integrals.

Nov. 27/17: Applications of Triple integrals. Triple integrals in cylinderical coordinates.

Nov. 29/17: Triple integrals in cylinderical coordinates and spherical coordinates.

Dec.1/17: Triple integrals with spherical coordinates. Review of the course Review . Class is finished.

Announcements For MATH253

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First Webwork and Homework on on the course website.

Additional Office Hour: Thursday (14/09), 4-5:20pm.

Additional Office Hours: 04/10, 05/10, 06/10, 10/10: 12noon-1pm

Additional Office Hours: MWF, 12-1pm.

Additional Office Hours: MTWThuF, 12-1pm.

Office Hours all day: Nov. 27-Dec. 5

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