Chapter 1 Real number system and functions 1.1 Real number system 1.2 Inequalities 1.3 Functions Chapter 2 Sequence Limit 2.1 Concept of sequence limit 2.2 Properties of convergent sequences 2.3 Fundamental theorems of sequenqe limit 2.4 Upper limit and lower limit of a sequence Chapter 3 Function limits and continuity 3.1 Concept of function limits 3.2 Properties of function limits 3.3 Two important limits 3.4 Infinitesimal and infinity 3.5 Concept of continuity 3.6 Properties of continuous functions 3.7 Continuity of primary functions 3.8 Uniform continuity Chapter 4 Derivatives and differentials 4.1 Concept of derivatives 4.2 Computation of derivatives 4.3 Differentials 4.4 Derivatives and differentials of higher order Chapter 5 Mean value theorems and applications of derivative 5.1 Mean value theorems 5.2 Monotony and extremum of functions 5.3 Graph of a function 5.4 L'Hospital rules 5.5 Newton-Raphson method Chapter 6 Indefinite integrals 6.1 Concept of indefinite integrals and fundamental formulas 6.2 Techniques of integration 6.3 Integration of some special kinds of functions Chapter 7 Definite integrals 7.1 Concept of definite integrals 7.2 Properties of definite integrals 7.3 The fundamental theorems of calculus 7.4 Integration techniques of definite integrals 7.5 Improper integrals 7.6 Numerical integration Chapter 8 Applications of definite integrals 8.1 Applications in geometry 8.2 Applications in physics Chapter 9 Preliminary of differential equations 9.1 Basic concepts of differential equations 9.2 Differential equations of first-order ……
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