MATH253-102 : Multivariable Calculus (1st term 2019/2020)
Lecture I: Monday 11am--12noon, BUCH-A201.
Lecture II: Wednesday 11am--12noon, BUCH-A201.
Lecture III: Friday 11am--12noon, BUCH-A201.
Office Hours: Every Monday, Wednesday, 3:30pm-5:30pm, LSK 303B.
TA: TBA
Course website: www.math.ubc.ca/~jbryan, or https://canvas.ubc.ca/courses/45638
Textbook For MATH253-102
Please refer to Canvas www.math.ubc.ca/~jbryan, or https://canvas.ubc.ca/courses/45638.
Downloads For MATH253-102
Please refer to www.math.ubc.ca/~jbryan, or https://canvas.ubc.ca/courses/45638
Updates For MATH253-102
Please refer to www.math.ubc.ca/~jbryan, or https://canvas.ubc.ca/courses/45638
Sept.4: coordinates systems, planes, lines, distances, spheres, vectors (introduction)
Sept. 6: dot-product. Angle and projection. Examples.
Sept. 9: cross product and its properties. Two application examples:area, normal vector to a plane.
Sept. 11: Equations of lines and planes.
Sept. 13: Distance between a point and a plane; distance between two parallel planes; distance between a point and a line. Start on Quadric surfaces. Cylinders.
Sept. 16: Classification of Quadric surfaces. Slicing and contours. Definition of functions of two variables.
Sept. 18: Contours. 11 examples. limits and continuity of functions of two variables.
Sept. 20: Limits, continuity, partial derivatives. Examples. Notes on Sept. 20
Sept. 23: Computations of 1st and 2nd order derivatives. Implicit function derivatives.
Sept 25: Midterm I
Sept 27: Examples of computing higher order derivatives (explicit and implicit). Applications to three typical partial differential equations. special solutions. Start on linear approximations.
Sept. 30: Tangent lines, tangent planes. Examples. Tangent plane approximations. Examples.
Oct. 2: Total differentials. Chain Rule.
Oct. 4: Implicit Function Differentiations. Directional derivatives.
Oct. 7: Direction derivatives, maximum rate of change, minimum, zero rate of change. Application of steepest descent.
Oct. 9: Gradient, directional derivative for functions fo three variables. Surfaces given by implicit functions. Applications to tangenet plane.
Oct. 11: critical points. computations of critical points. second order derivative test.
Oct. 16: Midterm II
Oct. 18: classification of critical points. Global max/Global min.
Oct. 21: Absolute Max/Min. Examples. Method of Lagrange Multipliers.
Oct. 23: More examples of Absolute Max/Min., and Method of Lagrange Multipliers.
Oct. 25: Two examples of Method of Multiplies. Integrals.
Oct. 28: Double Integrals. Fubini Theorem.
Oct. 30: Type I Domain. Type II Domain.
Nov. 1: Type I and Type II double integrals. Exchange of the order of integrations.
Nov. 4: Exchange order of integrations. Introduction to polar coordinates. Double integrals in polar coordinates.
Nov. 6: Double integrals in polar coordinates. Examples of changing to polar coordinates.
Nov. 8: Review for Midterm 3. Applications of Double Integrals.
Nov. 13: Midterm III
Nov. 15: Center of Mass.
Nov. 18: Surface Area.
Nov. 20: Triple integrals. Type 1,2,3 domains. Exchange order of integrations.
Nov. 22: Exchange order of triple integrals in Cartesian coordinates.
Nov. 25: Triple integrals in cylinderical coordinates. Applications of Tripe integrals.
Nov. 27: Triple integrals in spherical coordinates.
Nov. 29: Triple integrals in cylinderical and spherical coordinates.
Announcements For MATH253-102
Webwork 1 has been posted on Canvas.
Please refer to Canvas www.math.ubc.ca/~jbryan, or https://canvas.ubc.ca/courses/45638
Coverage of Midterm 1: dot-product and cross-product of vectors; angle between two lines; angle between a line and a plane; intersection of lines and planes; distance between two planes; distances between a point and a line; contour of quadric surfaces
New office Hours on September 27: 3-6pm
Office Hours in the week of September 30-Oct. 4: Oct. 2, 2-3pm, Oct. 3, 10-4pm, Oct. 4 2-3pm.
Office hours on Oct. 14: 1-3pm
Office hours in the exam period: Dec. 2, 3, Dec. 12, 13, 16, 17,
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