Week
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Topics covered
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1
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Sequences and Convergence; Infinite Series; Convergence Tests for Positive Series; Absolute and Conditional Convergence
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2
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Power Series; Taylor and Maclaurin Series; Applications of Taylor and Maclaurin Series; The Binomial Theorem and Binomial Series
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3
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Analytic Geometry in Three Dimensions; Vectors ; The Cross Product in 3-Space; Planes and Lines
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4
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Quadric Surfaces; Conics (only Classifying General Conics); Vector Functions of One Variable; Curves and Parametrizations; Arc Length and Surface Area (up to Areas of Surfaces of Revolution)
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5
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Functions of Several Variables; Limits and Continuity
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6
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Partial Derivatives (omit Distance from a Point to a Surface); Higher-Order Derivatives; The Chain Rule (omit Homogeneous Functions); Linear Approximations, Differentiability, and Differentials; (up to Differentials in Applications)
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7
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Gradients and Directional Derivatives; Implicit Functions; Taylor Series and Approximations (omit Approximating Implicit Functions)
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8
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Extreme Values; Extreme Values of Functions Defined on Restricted Domains (omit Linear Programming); Lagrange Multipliers (omit Nonlinear Programming)
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9
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Parametric Problems (only Differentiating Integrals with Parameters); Double Integrals; Iteration of Double Integrals in Cartesian Coordinates; Improper Integrals and a Mean-Value Theorem
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10
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Polar Coordinates and Polar Curves (omit Polar Conics); Double Integrals in Polar Coordinates; Slopes, Areas, and Arc Lengths for Polar Curves (only Areas Bounded by Polar Curves); Triple Integrals
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11
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Cylindrical and Spherical Coordinates; Change of Variables in Triple Integrals
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12
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Vector and Scalar Fields(up to Fields Lines); Conservative Fields (omit Sources, Sinks, and Dipoles); Line Integrals; Line Integrals of Vector Fields
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13
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Surfaces and Surface Integrals (omit The Attraction of a Spherical Shell ); Arc Length and Surface Area (only Areas of Surfaces of Revolution); Oriented Surfaces and Flux Integrals
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14
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Gradient, Divergence, and Curl (up to Interpretation of the Divergence); Some Identities Involving Grad, Div, and Curl; Green's Theorem in the Plane.
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