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The True Fundamentals
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The Language of Mathematics
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The Importance of Definitions
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Keeping consistent language
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The world of mathematical definitions
Understanding the Basics of Axioms, Theorems, and Proofs
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Axioms
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Inverses and Their Implications
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A brief mathematical interlude
Understanding inverses
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Part 2 | Sets and Numbers
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Chapter 1 | Sets of Objects
Chapter 2 | Sets of Numbers
Chapter 3 | Operations on Numbers
Algebra
Part 1 | Adjusting to Algebra
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Chapter 1 | An Introduction to Algebra
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Section 1.7 | Solving Algebraic Equations in One Variable
Part 2 | Developmental Linear Algebra
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Preface
Chapter 1 | Linear Equations in One Variable and Their Applications
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Section 1.3 | Applications Involving Solutions of Linear Equations in One Variable: Percent
Chapter 2 | Linear Equations in Two Variables and Their Applications
Chapter 3 | Systems of Linear Equations
Chapter 4 | Linear Inequalities, Systems of Linear Inequalities, and Their Applications
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Section 4.2 | Solving Absolute Value Equations and Inequalities
Part 3 | Functions
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Chapter 1 | Functions
Chapter 2 | Connecting Concepts - From Linear Equations to Linear Functions
Part 4 | Exponential Algebra
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Chapter 1 | Exponents
Chapter 2 | Radical Expressions and Equations
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Radicals and Roots
Chapter 3 | Exponential and Logarithmic Functions
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Exponentials and Logarithms
Part 5 | Polynomial Algebra
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Chapter 1 | Introduction to Polynomials and Polynomial Functions
Chapter 2 | Factoring Polynomials
Chapter 3 | Solving Polynomial Equations
Chapter 4 | Applications and Graphing Quadratic and Polynomial Functions
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Section 4.11: Solving Polynomial Inequalities
Quadratics
Chapter 5 | Conic Sections
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Section 5.1 | An Introduction to Conic Sections
Section 5.2 | Parabolas Revisited
Section 5.3 | Ellipses
Section 5.4 | Hyperbolas
Part 6 | Rational Algebra
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Chapter 1 | Ratios of Polynomials
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Rationals
Section 1.7: Problem Solving Using Rational Equations
Section 1.8: Inverse, Joint, and Combined Variation
Calculus
Part 1 | Limits
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The Collection of Limit Proofs
Part 2 | Total Derivatives
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The Collection of Derivative Proofs
Part 3 | Single Integrals
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Chapter 2 | Techniques of Integration
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Section 2.7 | Basic Numerical Integration
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2.7.1 | What is numerical integration?
2.7.2 | An overview of basic numerical integration techniques
2.7.3 | Integrating numerically
Section 2.9 | Improper Integrals
Section 2.10 | The Integral Comparison Theorem
Section 2.11 | A Summary of Integration Techniques
Chapter 3 | Applications of Integration
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Section 3.2 | Fluid Pressure
Section 3.3 | Center of Mass
Section 3.4 | Average Value of a Function
Section 3.5 | Lengths of Curves
Section 3.6 | Surface Area of Revolved Objects
Chapter 4 | The Calculus of Parametric Curves
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Section 4.1 | Derivatives of Parametric Curves
Section 4.2 | Areas Defined by Parametric Curves
Section 4.3 | Curve Lengths and Surface Areas of Parametric Curves
Part 4 | Infinite Sequences and Series
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Chapter 1 | Convergence and Divergence of Series
Chapter 2 | Power Series
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Theorem and Proof | Taylor's Inequality
Part 5 | Partial Derivatives
Part 6 | Multiple Integrals
Part 7 | Vectors and Vector Calculus
Differential Equations
The Basics of Differential Equations
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Lecture 1 The Language of Differential Equations
Lecture 2 An Introduction to Solutions of Differential Equations
Laplace Transforms
Final Exam Review
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First-Order ODEs
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Factoring Example Level 6
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A simple equation is any equation involving a single occurrence of a variable, either as the argument of a function or not, or multiple occurrences of a variable that, when simplified, reduce to a single occurrence.