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Calculus2

Hisashi Yokota

• 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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