Short description Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations.
From the contents Preface.
0.1 Short Introduction.
0.2 Introduction.
Acknowledgments.
1 Calculus I.
1.1 A Sketch of the Development of Rigor in Calculus and Analysis.
1.2 Basics.
1.3 Limits and Continuous Functions.
1.4 Differentiation.
1.5 Applications of Differentiation.
1.6 Riemann Integration.
2 Calculus II.
2.1 Techniques of Integration.
2.2 Improper Integrals.
2.3 Series of Real Numbers.
2.4 Series of Functions.
2.5 Analytical Geometry and Elementary Vector Calculus.
3 Calculus III.
3.1 Vector-Valued Functions of Several Variables.
3.2 Derivatives of Vector-Valued Functions of Several Variables.
3.3 Applications of Differentiation.
3.4 Integration of Functions of Several Variables.
3.5 Vector Calculus.
3.6 Generalizations of the Fundamental Theorem of Calculus.
Appendix A.
A.1 Construction of the Real-Number System.
A.2 The Lebesgue Criterion for Riemann Integrability.
