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Maximum and-Minimum of a Function of Several Variables The Equations of a Curve in Space 2. The Equation of a Tangent to a Curve. The Equation of a Normal Plane 3. Rules for Differentiating Vectors Vector Functions 4. The Curvature of a Curve. The Principal Normal Osculating Plane. Torsion 6. Antiderivative and the Indefinite Integral 2. Table of Integrals 3. Some Properties of an Indefinite Integral 4.
Integration by Substitution Change of Variable 5. Integrals of Functions Containing a Quadratic Trinomial 6. Integration by Parts 7. Rational Fractions. Partial Rational Fractions and Their Integration 8.
Decomposition of a Rational Fraction into Partial Fractions Integration of Rational Fractions Integrals of Irrational Functions Integration of Binomial Differentials Integration of Certain Classes of Trigonometric Functions Statement of the Problem.
The Lower and Upper Integral Sums. The Definite Integral 3. Basic Properties o? Evaluating a Definite Integral. Newton-Leibniz Formula 5. Changing the Variable in the Definite Integral 6. Improper Integrals 8. Approximating Definite Integrals 9. Computing Areas in Rectangular Coordinates 2.
The Arc Length of a Curve. The Volume of a Solid of Revolution 6. The Surface of a Solid of Revolution 7. Computing Work by the Definite Integral 8.
The Equation of a Catenary 2. Equations with Separated and Separable Variables. The Problem of the Disintegration of Radium 5. Homogeneous First-Order Equations 6. Equations Reducible to Homogeneous Equations 7. First-Order Linear Equations 8. Exact Differential Equations Integrating Factor The Envelope of a Family of Curves Orthogonal and Isogonal Trajectories Higher-Order Differential Equations Fundamentals Homogeneous Linear Equations.
Definitions and General Properties Nonhomogeneous Second-Order Linear Equations Higher-Order Nonhomogeneous Linear Equations The Differential -Equation of Mechanical Vibrations Systems of Ordinary Differential Equations Adams Method Calculating Double Integrals 3. Calculating Double Integrals Continued 4. The Double Integral in Polar Coordinates 6. Computing the Area of a Surface 8.
Triple Integrals Evaluating a Triple Integral Change of Variables in a Triple Integral Computing Integrals Dependent on a Parameter. Line Integrals 2. Evaluating a Line Integral 3. Surface Integrals. Evaluating Surface Integrals 7. Sum of a Series 2. Necessary Condition for Convergence of a Series 3. Comparing Series with Positive Terms 4.
The Integral Test for Convergence of a Series. Alternating Series. PIus-and-Minus Series. Absolute and Contitional Convergence Functional Series The Continuity of the Sum of a Series Integration and Differentiation of Series Power Series. Interval of Convergence Differentiation of Power Series Examples of Expansion of Functions in Series The Binomial Series Computing Logarithms Integrating Differential Equations by Means of Series Statement of the Problem 2.
Expansions of Functions in Fourier Series 3. Fourier Series for Even and Odd Functions 5. The Dirichlet Integral 9. Practical Harmonic Analysis Fourier Integral Basic Types of Equations of Mathematical Physics. Derivation of the Equation of Oscillations of a String. Formulation of the Boundary-Value Problem. Derivation of Equations of Electric Oscillations in Wires : 3. The Equation for Propagation of Heat in a Rod. Formulation of the Boundary-Value Problem 5.
Heat Propagation in Space 6. Propagation of Heat in an Unbounded Rod 8. Stating Boundary-Value Problems 9. The Laplace Equation in Cylindrical Coordinates.
Differential And Integral Calculus - N Piskunov.pdf
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Differential and Integral Calculus