Semestre 1

Chapter 1: Methods of Mathematical Reasoning
1-1 Direct Reasoning
1-2 Proof by contrapositive
1-3 Reductio ad absurdum
1-4 Proof by Counterexample
1-5 Proof by Induction
Chapter 2: Sets, Relations, and Applications
2-1 Set Theory
2-2 Equivalence Relations and Partial Orders
2-3 Injective, Surjective, Bijective Functions: Definition of a Function, Direct Image, Inverse Image, Characteristics of an Application
Chapter 3: Real functions of one real variable
3-1 Limiting process; Continuity of a Function
3-2 Derivative and Differentiability of a Function
Chapter 4: Application to Elementary Functions
4-1 Power Functions
4-2 Logarithmic Functions
4-3 Exponential Functions
4-4 Hyperbolic Functions
4-5 Trigonometric Functions
4-6 Inverse Functions
Chapter 5: Taylor Series Expansion
5-1 Taylor's Formula
5-2 Taylor's/Maclaurin’s Expansions
5-3 Applications
Chapter 6: Linear Algebra
6-1 Laws and Internal Composition
6-2 Vector Spaces, Basis, Dimension (Definitions and Elementary Properties)
6-3 Linear Transformation, Kernel, Image, Rank