MAT 235Y: Calculus II (LEC0102/9102)

Lecture notes:

• Lecture 1 (September 10). Conic sections: ellipse, parabola, hyperbola
• Lecture 2 (September 14). Conic sections: ellipse, parabola, hyperbola
• Lecture 3 (September 16). Curves defined by parametric equations
• Lecture 4 (September 17). Calculus with parametric curves
• Lecture 5 (September 21). Calculus with parametric curves
• Lecture 6 (September 23). Polar coordinates
• Lecture 7 (September 24). Polar curves
• Lecture 8 (September 28). Calculus with polar curves
• Lecture 9 (September 30). Areas and lengths in polar coordinates
• Lecture 10 (October 1). 3D space and vectors
• Lecture 11 (October 5). Vector norm and dot product
• Lecture 12 (October 7). Dot product and cross product
• Lecture 13 (October 8). Cross product
• Lecture 14 (October 14). Scalar triple product
• Lecture 15 (October 15). Lines in 3D
• Lecture 16 (October 19). Planes in 3D
• Lecture 17 (October 21). Quadric surfaces
• Lecture 18 (October 22). Space curves
• Lecture 19 (October 26). Space curves: velocity and acceleration
• Lecture 20 (October 28). Functions of several variables
• Lecture 21 (October 29). Limits and continuity
• Lecture 22 (November 2). Limits and continuity
• Lecture 23 (November 4). Partial derivatives
• Lecture 24 (November 5). Review
• Lecture 25 (November 16). More partial derivatives
• Lecture 26 (November 18). Tangent planes & Linear approximations
• Lecture 27 (November 19). Linear approximations and differentiability
• Lecture 28 (November 23). Multivariable chain rule
• Lecture 29 (November 25). Applications of the chain rule
• Lecture 30 (November 26). Directional derivatives
• Lecture 31 (November 30). Significance of gradient
• Lecture 32 (December 2). Maximum and minimum values
• Lecture 33 (December 3). Local extrema
• Lecture 34 (December 7). Global extrema
• Lecture 35 (December 9). Lagrange multipliers
• Lecture 36 (January 11). Lagrange multipliers with 2 constraints
• Lecture 37 (January 13). Review of the definite integral
• Lecture 38 (January 14). Double integrals over rectangles
• Lecture 39 (January 18). Double integrals over general regions
• Lecture 40 (January 20). Double integrals in polar coordinates
• Lecture 41 (January 21). Review
• Lecture 42 (January 25). Double integrals in polar coordinates
• Lecture 43 (January 27). Applications of double integrals
• Lecture 44 (January 28). Surface area
• Lecture 45 (February 1). Triple integrals
• Lecture 46 (February 3). Triple integrals
• Lecture 47 (February 4). Triple integrals in cylindrical coordinates
• Lecture 48 (February 8). Triple integrals in spherical coordinates
• Lecture 49 (February 10). Triple integrals in spherical coordinates
• Lecture 50 (February 11). Jacobian
• Lecture 51 (February 22). Jacobian and change of variables in multiple integrals
• Lecture 52 (February 24). Vector fields
• Lecture 53 (February 25). Vector fields
• Lecture 54 (March 1). Line integral with respect to arc length
• Lecture 55 (March 3). Line integral of a vector field
• Lecture 56 (March 4). Line integral with respect to x and y
• Lecture 57 (March 8). Fundamental theorem of line integrals
• Lecture 58 (March 10). Fundamental theorem of line integrals
• Lecture 59 (March 11). Review
• Lecture 60 (March 15). Green's theorem
• Lecture 61 (March 17). Green's theorem
• Lecture 62 (March 18). Curl
• Lecture 63 (March 22). Divergence
• Lecture 64 (March 24). Vector forms of Green's theorem
• Lecture 65 (March 25). Parametric surfaces
• Lecture 66 (March 29). Parametric surfaces
• Lecture 67 (March 31). Surface integral of a function
• Lecture 68 (April 1). Orientable surfaces
• Lecture 69 (April 5). Surface integral of a vector field
• Lecture 70 (April 7). Stokes' theorem
• Lecture 71 (April 8). Divergence theorem