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Contents
Contents
Index
Calculus2
Hisashi Yokota
Exercises in Introduction to Calculus2
Contents
Partial Differentiation
Function of Several Variavles
Limit of Functions of Two Variables
Partial Derivatives
Total Differential and Tangent Plane
Tangent Plane and Normal Vector
Partial Differentiation of Composite Functions
Higher Order Partial Derivatives
Extreme Values of Function of Two Variables
Taylor Theorem for Two Variables
Conditional Extrema
Implicit Functions
Lagrange Multiplier
Multiple Integrals
Double Integrals
Repeated Integrals
Change of Variables
Improper Double Integrals
Application of Double Integrals
Area
Surface Area
Volume of Solid
Triple Integrals
ANSWERS
0.2 INEQUALITIES
1.1 Functions
1.2 Trigonometric Functions
1.3 Limits of Functions
1.4 Continuous functions
1.5 Sequences
1.6 Transcendental functions
2.1 Derivatives
2.2 Differential Formulas
2.3 Higher order dirivatives
2.4 Mean value theorem
2.5 Curve sketching
2.6 Limit of indeterminate form
3.1 Antiderivatives
3.2 Integration by substitution
3.3 Integration by parts
3.4 Integration of rational functions
3.5 Integration of trigonometric functions
3.6 Integration of irrational functions
3.7 Definite integrals
3.8 Evaluation of definite integrals
3.9 Improper integrals
3.10 Application of definite integrals
4.1 Function of several variables
4.2 Partial derivatives
4.3 Limit of functions of two variables
4.4 Total differential and tangent plane
4.5 Directional derivatives
4.6 Partial differentiation of composite functions
4.7 Extreme values of functions of two variables
4.8 Implicit functions
4.9 Conditional extrema
5.2 Repeated integrals
5.3 Change of variables
5.4 Inproper integrals
5.5 Application of double integrals
5.6 Triple integrals
ANSWERS B
1.1 FUNCTIONS
1.2 Trigonometric Functions
1.3 Limits
1.4 Continuous functions
1.5 Sequences
1.6 Transcendental functions
2.1 Derivatives
2.2 Differentiation formulas
2.3 Higher order derivatives
2.4 Properties of functions
2.5 Curve sketching
2.6 Limits of indeterminate form
2.7 Taylor's theorem
3.1 Antiderivatives
3.2 Integration by substitution
3.3 Integration by parts
3.4 Integration of rational functions
3.5 Integration of trigonometric functions
3.6 Integration of irrational functions
3.7 Definite integrals
3.8 Evaluation of integrals
3.9 Improper integrals
3.10 Application of integrals
4.1 Functions of several variables
4.2 Partial derivatives
4.3 Limit of functions of two variables
4.4 Total differentials
4.5 Directional derivatives
4.6 Partial differentiation of composite functions
4.7 Extreme value of functions of two variables
4.8 Implicit functions
4.9 Lagrange's multiplier
5.2 Repeated interals
5.3 Change of variables
5.4 Improper integrals
5.5 Application of double integrals
5.6 Triple integrals
Index
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