Advanced Calculus Lecture Notes for Mathematics by James S. Muldowney

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Advanced Calculus Lecture Notes for Mathematics written by
James S. Muldowney
cover the following topics.

The Real Number system & Finite Dimensional Cartesian Space The Real Number System R (Fields, Ordered Fields), Complete Ordered Field, Properties of R, Cartesian Spaces (Functions, Convexity), Topology

Limits, Continuity, and Differentiation Sequences, Continuity, Global Properties of Continuous Functions, Uniform Continuity, Limits, Differentiation of real valued functions of a real variable

Riemann Integration Content and the Riemann Integral (Partition of I, Riemann Sums, Exercises), Cauchy Criteria and Properties of Integrals, Evaluation of Integrals (Real valued functions of a real variable, Real valued functions on R^2, Real valued functions on R^n)

Differentiation 0f Functions of Several Variables Preliminaries (Linear Functions, Straight Lines and Curves), The Directional Derivative and the Differential, Differentiation Rules, Partial Derivatives of Higher Order, Min-Max Theory, Local Properties of C, Implicit Function Theorem (Dimension, Application: Lagrange Multipliers)

Further Topics in Integration Changes of Variables in Integrals, Integration on Curves and Surfaces, Curves (1-surfaces), Surfaces (2-surfaces)