| Week | Topics | Study Materials | Materials |
| 1 |
Sequences, Infinite Series, The Integral Test, Comparison Tests, Absolute Convergence: The Ratio and Root Tests
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| 2 |
Alternating Series and Conditional Convergence, Power Series, Taylor and Maclaurin Series, Convergence of Taylor Series, The Binomial Series and Applications of Taylor Series
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| 3 |
Parametrizations of Plane Curves, Calculus with Parametric Curves, Polar Coordinates, Graphing in Polar Coordinates
11.5 Areas and Lengths in Polar Coordinates
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| 4 |
Three-Dimensional Coordinate Systems, Vectors, The Dot Product, The Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces
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| 5 |
Curves in Space and Their Tangents, Integrals of Vector Functions; Projectile Motion, Arc Length in Space, Curvature and Normal Vectors of a Curve,Tangential and Normal Components of Acceleration
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| 6 |
Functions of Several Variables, Limits and Continuity in Higher Dimensions, Partial Derivatives, The Chain Rule, Directional Derivatives and Gradient Vectors
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| 7 |
Tangent Planes and Differentials, Extreme Values and Saddle Points, Lagrange Multipliers, Taylor’s Formula for Two Variables, Partial Derivatives with Constrained Variables
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| 8 |
Double and Iterated Integrals over Rectangles, Double Integrals over General Regions, Area by Double Integration, Double Integrals in Polar Form
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| 9 |
AGU-LFW
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| 10 |
Triple Integrals in Rectangular Coordinates, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals
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| 11 |
Spring Break
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| 12 |
Line Integrals, Vector Fields and Line Integrals: Work, Circulation, and Flux, Path Independence, Conservative Fields, and Potential Functions
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| 13 |
Green’s Theorem in the Plane, Surfaces and Area, Surface Integrals
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| 14 |
Stoke’s Theorem, The divergence theory and unified Theory
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| 15 |
Review of Materials and Problem Solving
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| 16 |
Final Exam
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