This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.
I: Review of Basic Material. Numbers and Functions. Graphs and Curves. II: Differention and Elementary Functions. The Derivative. Sine and Cosine. The Mean Value Theorem. Sketching Curves. Inverse Functions Exponents and Logarithms. III: Integration. Integration. Properties of the Integral. Techniques of Integration. Applications of Integration. IV: Taylor's Formula and Series. Taylor's Formula. Series. Appendix. V: Functions of Several Variables. Vectors. Differention of Vectors. Functions of Several Variables. The Chain Rule and the Gradient.