Integration of Rational Functions Note. This problem shows that a study of domains of definition of a function facilitates the solution of equations, inequalities, etc. Search results The principal linear part of this increment A x Ax is called the diffe- rential and is denoted df x or dy. Find the roots of the following equations.
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Definition of the Derivative 98 2. Differentiation of Explicit Functions 2. Successive Differentiation of Explicit Functions. Leibniz Formula 2. Applications of the Derivative 2. The Differential of a Function. Application to Approximate Computations 2. Basic Theorems on Differentiable Functions 3.
Evaluation of Indeterminate Forms. Application to Approximate Calculations 3. Testing a Function for Monotonicity 3. Maxima and Minima of a Function 3. Finding the Greatest and the Least Values of a Function 3. Solving Problems in Geometry and Physics 3.
Convexity and Concavity of a Curve. Points of Inflection 3. Asymptotes 3. Approximate Solution of Algebraic and Transcendental Equations 3. Additional Problems Indefinite Integrals. Basic Methods of Integration 4. Direct Integration and the Method of Expansion 4. Integration by Substitution 4. Integration by Parts 4. Integration of Rational Functions 5.
Integration of Certain Irrational Expressions 5. Other Methods of Integrating IrrationalExpressions 5. Integration of a Binomial Differential 5. Integration of Trigonometric and Hyperbolic Functions 5. Integration of Other Transcendental Functions 5. Statement of the Problem. The Lower and Upper Integral Sums 6. Estimating an Integral.
Changing the Variable in a Definite Integral 6. Integration by Parts. Reduction Formulas 6. Approximating Definite Integrals. Additional Problems Applications of the Definite Integral 7. Finding Average Values of a Function 7. Computing Areas in Rectangular Coordinates 7. Computing Areas with Parametrically Represented Boundaries 7. Computing the Volume of a Solid 7.
Area of Surface of Revolution 7. Geometrical Applications of the Definite Integral 7. Computing Static Moments and Moments of Inertia. Determining Coordinates of the Centre of Gravity 7. Additional Problems
PROBLEMS IN CALCULUS OF ONE VARIABLE BY I.A.MARON
The book is intended as an introduction to calculus, helping students in class and class understand the mathematical basis required for an additional or more advanced course. The book covers mathematical analysis, limits of a function, differential calculus, integral calculus, applications of differentiation and integration and improper integrals among other associated topics. The book is an indispensable resource for students aspiring for admission into one of the Indian Institutes of Technology for a Bachelor program in Engineering. About I. Maron I.
Problems In Calculus Of One Variable by I. A. Maron
Definition of the Derivative 98 2. Differentiation of Explicit Functions 2. Successive Differentiation of Explicit Functions. Leibniz Formula 2.
I A Maron Books