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MAA00A1 1A Introduction to mathematical analysis

This course features a somewhat gentler introduction to the standard Analysis I material than the traditional course. It emphasizes one-variable analysis and de-emphasizes point-set topology. It assumes students did well in a standard single-variable calculus course. The textbook is written in a user-friendly style, discursive rather than brief, making the book usable for self-study.

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Analysis I MIT students may choose to take one of three versions of Option B Option C Institutional Subscription. Free Shipping Free global shipping No minimum order.

Preface List of Symbols and Notations I. Fundamental Ideas and Assumptions 1.


An Introduction to Mathematical Analysis by John B. Reade

Introduction 2. Assumptions Relating to the Field Operations 3.

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  • Assumptions Relating to the Ordering of the Real Numbers 4. Mathematical Induction 5.

    Functions II. Limits and Continuity 7.

    Detailed Course Information

    Limits of Real Functions on the Positive Integers 8. Elementary Topological Ideas Limits of Real Functions at Finite Points Continuity Differentiability Derivatives General Theorems Concerning Real Functions Maxima, Minima and Convexity Complex Numbers and Functions IV.

    Debussy's use of the Fibonacci sequence Essay

    Infinite Series Elementary Properties of Infinite Series Series with Non-Negative Terms Absolute and Conditional Convergence Functions Defined by Power Series General Theory of Power Series Real Power Series The Exponential and Logarithmic Functions The Trigonometric Functions The Hyperbolic Functions Complex Indices VI. Integration The Indefinite Integral Interval Functions and Functions of Bounded Variation The Riemann-Stieltjes Integral The Riemann Integral Curves