This text contains a consistent and complete exposition of a single variable calculus course for any university in the world. The readers will find transcendental functions introduced at the very beginning, the notion of a sequence and its limit studied before a limit of a function is introduced.

• Theorems with complete proofs, numerous examples and practice problems of various order of difficulties • Enlarged coverge of integration techniques with applications to geometric problems • Systems exposition of complex numbers merged into the main course, together with proof of the fundamental theorem of algebra and Cardans’s formulas for solving algebraic equations of order 3 and 4 • Set of Maple Labs, allows students to acquire the ability to use the Maplemathematical software for solving complex calculus problems

Real Numbers: Historical Remarks/Extension of Rational Numbers to Real Numbers\Axioms of Real Numbers, Absolute Values and the Principle of Mathematical Induction/Further Properties of Real Numbers: Powers and Logarithms/Complex Numbers/Review and Supplementary Problems/ Sequences: What is a Sequences/Convergence of Sequences and the Notion of a Limit/The Number /Further Properties of Limits/Complex Sequences/ Review and Supplementary Problems/ Limit of a function and Continuity: Functions and Their Properties/Definition of the Limit of a Function/Continuous Functions/Further Properties of Continuous Functions/Continuity of Elementary Functions/Functions of Complex Variable/Review and Supplementary Problems/ Derivatives and Differentials: Derivative and its Properties/Differential/Fundamental Properties of Differentiable Functions/ Hopital Rule/Further Applications of Derivatives/Higher Order Derivatives/The Taylor Formula/Convex Functions and Investigation of Graphs/Newtons’s Approximation Method/Fundamental Theorem of Algebra/Review and Supplementary Problesm/ Anti derivatives and Indefinite Integrals: Antiderivatives and the Definition of an Indefinite Integral/Integration Rules/Integration of Rational Functions/Integration of Certain Irrational Expressins/Integration of Trigonometric and Hyperbolic Functions/Solving Algebraic Equations/ Review and Supplementary Problems / Definite Integrals: Definition of the Definite Integral and Conditions for Integrability/Properties of Definite Integrals and the Fundamental Theorem of Calculus/Approximate Integration/Improper Integrals/Review and Supplementary Problems/Applications of the Definite Integrals:Arc Length of a Curve/Computing Areas Bounded by Curves/Computation of Volumes/Area of a Surface of Revolution/Review and Supplementary Problems / Infinite Series and Power Series: Infinite Series/Absolute and Conditional Convergence of Infinite Series/Power Series/Review and Supplementary Problems/ Solutions of Selected Problems/ Appendix 1: Elements of Linear Algebra/Appendix 2: Maple V Labs (by Liping Liu / Refereences / Index

Undergraduate students and Teachers