Introduction to differential calculus : systematic studies with engineering applications for beginners - Rohde, Ulrich L. (Wiley, 2012)
Machine generated contents note: Chapter One. From Arithmetic to Algebra. Chapter Two. The Concept of Function. Chapter Three. Discovery of Real Numbers (Through Traditional Algebra). Chapter Four. From Geometry to Co-ordinate Geometry. Chapter Five. Trigonometry and Trigonometric Functions. Chapter Six. More about Functions. Chapter Seven. (a): The Concept of Limit of a Function. Chapter Seven. (b): Methods for Computing Limits of Algebraic Functions. Chapter Eight. The Concept of Continuity of a Function and the Points of Discontinuity. Chapter Nine. The Idea of Derivative of a Function. Chapter Ten. Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions. Chapter Eleven. (a): Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions. Chapter Eleven. (b): Methods of Computing Limits of Trigonometric Functions. Chapter Twelve: Exponential Form(s) of a Positive Real Numbers and its Logarithms. Chapter Thirteen. (a): Exponential and Logarithmic Functions as Their Derivatives. Chapter Thirteen. (b): Methods for Computing Limits and Exponential and Logarithmic Functions. Chapter Fourteen. Inverse Trigonometric Functions and Their Derivatives. Chapter Fifteen. (a): Implicit Functions and Their Differentiation. Chapter Fifteen. (b): Parametric Functions and Their Differentiation. Chapter Sixteen. Differentials 'dy' and 'dx': Meanings and Applications. Chapter Seventeen. Derivatives and Differentials of Higher Order. Chapter Eighteen. Applications of Derivatives in Studying Motion in a Straight Line. Chapter Nineteen. (a): Increasing and Decreasing Functions and the Sign of the First Derivative. Chapter Nineteen. (b): Maximum and Minimum Values of a Function. Chapter Twenty. Rolle's Theorem and the Mean Value Theorem (MVT). Chapter Twenty One. The Generalized Mean Value Theorem (Cauchy's MVT), L'Hospital's Rule, and Its Applications. Chapter Twenty Two. Extending the Mean Value Theorem to Taylor's Formula: Taylor Polynomials for Certain Functions. Chapter Twenty Three. Hyperbolic Functions and Their Properties.