微積分統一教學網-模03-12班課程大綱

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微積分 1	第一週	2.1	The Tangent and Velocity Problems
		2.2	The Limit of a Function
		2.3	Calculating Limits Using the Limit Laws
	第二週	2.4	The Precise Definition of a Limit
		2.5	Continuity
		2.6	Limits at Infinity; Horizontal Asymptotes
	第三週	2.7	Derivatives and Rates of Change
	第三週	2.8	The Derivative as a Function
	第四週	3.1	Derivatives of Polynomials and Exponential Functions
		3.2	The Product and Quotient Rules
		3.3	Derivatives of Trigonometric Functions
	第五週	3.4	The Chain Rule
		3.5	Implicit Differentiation
		3.6	Derivatives of Logarithmic and Inverse Trigonometric Functions
	第六週 11/2(二)微積分1停修截止	3.9	Related Rates
		3.10	Linear Approximations and Differentials
		4.1	Maximum and Minimum Values
	第七週	4.2	The Mean Value Theorem
		4.3	What Derivatives Tell Us about the Shape of a Graph
		4.4	Indeterminate Forms and l'Hospital's Rule
	第八週	4.5	Summary of Curve Sketching
		4.7	Optimization Problems
		4.9	Antiderivatives
	期考 11/13(六) 考試以英文命題
微積分 2	第九週 11/23(二) 微積分2退選截止	5.1	The Area and Distance Problems
		5.2	The Definite Integral
		5.3	The Fundamental Theorem of Calculus
	第十週	5.4	Indefinite Integrals and the Net Change Theorem
	第十週	5.5	The Substitution Rule
	第十一週 12/7(二) 微積分2停修截止	6.1	Areas Between Curves
		6.2	Volumes
		6.3	Volumes by Cylindrical Shells
		6.5	Average Value of a Function
	第十二週	7.1	Integration by Parts
		7.2	Trigonometric Integrals
		7.3	Trigonometric Substitution
	第十三週	7.4	Integration of Rational Functions by Partial Fractions
		7.5	Strategy for Integration
		7.8	Improper Integrals
	第十四週	8.1	Arc Length
		8.2	Area of a Surface of Revolution (*)
		9.1	Modeling with Differential Equations
		9.3	Separable Equations
	第十五週	9.5	Linear Equations
		10.1	Curves Defined by Parametric Equations
		10.2	Calculus with Parametric Curves
	第十六週	10.3	Polar Coordinates
	第十六週	10.4	Calculus in Polar Coordinates
	期考1/9(日) 考試以英文命題

微積分 3	第一週	12.6	Cylinders and Quadric Surfaces
		14.1	Functions of Several Variables
		14.2	Limits and Continuity
	第二週	14.3	Partial Derivatives
	第二週	14.4	Tangent Planes and Linear Approximations
	第三週	14.5	The Chain Rule
		14.6	Directional Derivatives and the Gradient Vector
		14.7	Maximum and Minimum Values
	第四週	14.8	Lagrange Multipliers
		15.1	Double Integrals over Rectangles
		15.2	Double Integrals over General Regions
	第五週	15.3	Double Integrals in Polar Coordinates
	第五週	15.4	Applications of Double Integrals (教到 Moments and Center of Mass)
	第六週 3/25(五)微積分3停修截止	15.5	Surface Area
		15.6	Triple Integrals
		15.7	Triple Integrals in Cylindrical Coordinates
	第七週	15.8	Triple Integrals in Spherical Coordinates
	第七週	15.9	Change of Variables in Multiple Integrals
	第八週	緩衝時間
	期考 4/9(六) 考試以英文命題
微積分 4	第九週 4/15(五) 微積分4退選截止	16.1	Vector Fields
		16.2	Line Integrals
		16.3	The Fundamental Theorem for Line Integrals
	第十週	16.4	Green's Theorem
		16.5	Curl and Divergence
		16.6	Parametric Surfaces and Their Areas
	第十一週 4/29(五) 微積分4停修截止	16.7	Surface Integrals
		16.8	Stokes' Theorem
		16.9	The Divergence Theorem
	第十二週	16.10	Summary
		11.1	Sequences
		11.2	Series
	第十三週	11.3	The Integral Test and Estimates of Sums
		11.4	The Comparison Tests
		11.5	Alternating Series and Absolute Convergence
	第十四週	11.6	The Ratio and Root Tests
		11.7	Strategy for Testing Series
		11.8	Power Series
	第十五週	11.9	Representations of Functions as Power Series
		11.10	Taylor and Maclaurin Series
		11.11	Applications of Taylor Polynomials
	第十六週	緩衝時間
	期考 6/4(六) 考試以英文命題

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2022-04-22

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