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Week
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Topics
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Study Metarials
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1
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Pointwise and uniform convergence of sequences of functions
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R1. Section 1.1
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2
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Relationship between uniform convergence, integral and derivative
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R1. Section 1.2
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3
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Uniform convergence of series of functions and its relationship between integral and derivative
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R1. Section 1.3
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4
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Introduction to power series
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R1. Section 2.1
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5
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Derivative and integral of the power series
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R1. Section 2.2
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6
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Taylor and Maclaurin series, their
applications
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R1. Section 2.3
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7
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Vector-valued functions, limit and continuity of vector-valued functions
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R1. Section 3.1
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8
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The derivative of vector-valued functions
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R1. Section 3.2
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9
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Functions of several variables
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R1. Section 3.3
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10
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Functions of several variables, limits, and continuity for functions of several variables
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R1. Section 4.1
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11
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Partial derivatives, the chain rule and total differentials
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R1. Sections 4.2
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12
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Directional derivatives and derivatives of the implicit functions
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R1. Section 4.3
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13
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Taylor expansion of functions of two variables, Maxima and minima, Regional transforms, Functional Dependency,
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R1. Section 5.1
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14
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Vector fields, differentiation under the integral sign
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R1. Section 5.2
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