College Algebra: PART#2 – MATH 1314: Advanced Functions, Systems, and Matrices

About Course

This second part of the College Algebra MATH 1314 course delves into more advanced algebraic topics essential for students pursuing further studies in mathematics, science, and engineering. Building on algebraic foundations, this course explores exponential and logarithmic functions, systems of equations (including nonlinear and three-variable systems), matrices, and determinants. It also introduces powerful mathematical tools such as sequences, conic sections, and the binomial theorem—often reserved for Precalculus. The course provides students with deep theoretical understanding and practical problem-solving techniques. All topics are supported with visual, symbolic, and applied representations, allowing students to engage with the material meaningfully and prepare for higher-level math.

Master exponential and logarithmic equations and functions.
Use properties of logarithms to simplify and solve equations.
Analyze and solve systems of equations and inequalities, including nonlinear and three-variable systems.
Perform operations with matrices and apply them to solve systems using inverses and Cramer’s Rule.
Understand and apply determinants in various contexts.
Extend your learning with sequences, conic sections, and the binomial theorem.
Strengthen analytical and problem-solving skills for STEM fields.
Prepare for Precalculus, Calculus, and college-level science and engineering courses.

Course Content

1. Exponential and Logarithmic Functions
This topic focuses on two essential mathematical models—exponential and logarithmic functions. Students will explore growth and decay models, the relationship between exponential and logarithmic forms, and the application of properties of logarithms to solve real-world and theoretical problems.

1.1 Exponential Functions
1.2 Logarithmic Functions
1.3 Properties of Logarithms
1.4 Solving Exponential and Logarithmic Equations

2. Systems of Equations and Inequalities
This topic introduces students to systems of equations and inequalities in two, three, and nonlinear variables. Students will master both algebraic and graphical techniques to analyze solutions and develop logical problem-solving strategies.

3. Matrices and Determinants
This topic equips students with the ability to use matrices and determinants as tools for solving systems of equations and representing data. Students will learn matrix arithmetic, inverses, and determinant-based methods, including Cramer’s Rule.

4. Additional Topics of College Algebra
These optional advanced topics extend student learning and offer rich mathematical exploration. They introduce powerful mathematical structures that frequently appear in Precalculus, Calculus, and standardized exams like the SAT, ACT, and GRE.

About Course

What Will You Learn?

Course Content

1.1 Exponential Functions

1.2 Logarithmic Functions

1.3 Properties of Logarithms

1.4 Solving Exponential and Logarithmic Equations

2. Systems of Equations and Inequalities
This topic introduces students to systems of equations and inequalities in two, three, and nonlinear variables. Students will master both algebraic and graphical techniques to analyze solutions and develop logical problem-solving strategies.

2.1 Solving Systems of Linear Equations

2.2 Systems in Three Variables

2.3 Systems of Nonlinear Equations

2.4 Systems of Inequalities

3. Matrices and Determinants
This topic equips students with the ability to use matrices and determinants as tools for solving systems of equations and representing data. Students will learn matrix arithmetic, inverses, and determinant-based methods, including Cramer’s Rule.

3.1 Matrix Operations

3.2 The Inverse of a Matrix

3.3 Determinants and Cramer’s Rule

4. Additional Topics of College Algebra
These optional advanced topics extend student learning and offer rich mathematical exploration. They introduce powerful mathematical structures that frequently appear in Precalculus, Calculus, and standardized exams like the SAT, ACT, and GRE.

4.1 Sequences and Series

4.2 Conic Sections

4.3 Binomial Theorem

Systems of Equations: From Linear to Nonlinear Systems

Differentiation in Depth: Advanced Techniques & Transcendental Functions (3)

Logarithmic and Exponential Equations

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College Algebra: PART#2 – MATH 1314: Advanced Functions, Systems, and Matrices

About Course

What Will You Learn?

Course Content

1.1 Exponential Functions

1.2 Logarithmic Functions

1.3 Properties of Logarithms

1.4 Solving Exponential and Logarithmic Equations

2. Systems of Equations and Inequalities This topic introduces students to systems of equations and inequalities in two, three, and nonlinear variables. Students will master both algebraic and graphical techniques to analyze solutions and develop logical problem-solving strategies.

2.1 Solving Systems of Linear Equations

2.2 Systems in Three Variables

2.3 Systems of Nonlinear Equations

2.4 Systems of Inequalities

3. Matrices and Determinants This topic equips students with the ability to use matrices and determinants as tools for solving systems of equations and representing data. Students will learn matrix arithmetic, inverses, and determinant-based methods, including Cramer’s Rule.

3.1 Matrix Operations

3.2 The Inverse of a Matrix

3.3 Determinants and Cramer’s Rule

4. Additional Topics of College Algebra These optional advanced topics extend student learning and offer rich mathematical exploration. They introduce powerful mathematical structures that frequently appear in Precalculus, Calculus, and standardized exams like the SAT, ACT, and GRE.

4.1 Sequences and Series

4.2 Conic Sections

4.3 Binomial Theorem

Related Courses

Systems of Equations: From Linear to Nonlinear Systems

Differentiation in Depth: Advanced Techniques & Transcendental Functions (3)

Logarithmic and Exponential Equations

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2. Systems of Equations and Inequalities
This topic introduces students to systems of equations and inequalities in two, three, and nonlinear variables. Students will master both algebraic and graphical techniques to analyze solutions and develop logical problem-solving strategies.

3. Matrices and Determinants
This topic equips students with the ability to use matrices and determinants as tools for solving systems of equations and representing data. Students will learn matrix arithmetic, inverses, and determinant-based methods, including Cramer’s Rule.

4. Additional Topics of College Algebra
These optional advanced topics extend student learning and offer rich mathematical exploration. They introduce powerful mathematical structures that frequently appear in Precalculus, Calculus, and standardized exams like the SAT, ACT, and GRE.