Precalculus Building Concepts and Connections By Revathi Narasimhan
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Precalculus Building Concepts and Connections By Revathi Narasimhan

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1,118
File size
30.08 MB
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Digital PDF
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eBook[PDF]
About this ebook
The Precalculus: Building Concepts and Connections by Revathi Narasimhan takes a functions-focused approach to bridge algebra and trigonometry concepts for advanced calculus prep. [1, 2]
The textbook is structured into 10 core chapters that outline essential precalculus topics: [1]
1. Fundamental Algebra Review
  • Algebra Review: Consolidates fundamental algebraic mechanics, simplifying expressions, and solving core foundational equations before introducing higher-level functions. [1]
2. Functions and Graphs
  • The Coordinate System: Plotting, equations of lines, and coordinate geometry.
  • Introduction to Functions: Explicitly defining functions, exploring their graphs, and analyzing behaviors such as domain, range, intercepts, and rates of change.
  • Operations & Transformations: The algebra of functions (compositions) and graphical shifts, reflections, and scaling.
  • Linear Models: Linear functions, variation, and mathematical modeling applications. [1, 2]
3. Polynomial and Rational Functions
  • Polynomial Dynamics: Analyzing higher-degree polynomial equations, identifying real and complex zeros, and mapping structural turnarounds.
  • Rational Functions: Investigating horizontal, vertical, and slant asymptotes, alongside evaluating domain restrictions. [1]
4. Exponential and Logarithmic Functions
  • Inverse Relationships: Evaluating exponential and logarithmic growth models, properties of logarithms, and solving complex transcendental equations. [1]
5. Trigonometric Functions
  • The Unit Circle & Right Triangles: Developing trigonometry from fundamental angles, arc length, unit circle coordinates, and right-triangle applications.
  • Trig Graphs: Periodicity, amplitude, phase shifts, and modeling periodic behavior. [1, 2]
6. Trigonometric Identities and Equations
  • Analytic Trigonometry: Verifying core trigonometric identities (sum, difference, double-angle) and solving trigonometric equations over designated domains. [1]
7. Additional Topics in Trigonometry
  • Extended Applications: Law of Sines, Law of Cosines, polar coordinates, and vectors in two-dimensional space. [1]
8. Systems of Equations and Inequalities
  • Linear & Non-linear Systems: Methods for solving multi-variable systems (substitution, elimination, matrices) and graphing linear programming constraints. [1]
9. Conic Sections
  • Geometric Loci: Formulating algebraic definitions and graphing parabolas, ellipses, and hyperbolas centered both at and away from the origin. [1]
10. Advanced Algebraic Topics
  • Sequences & Series: Arithmetic and geometric sequences, series summation, mathematical induction, and the Binomial Theorem. [1]

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Topics

Consolidates fundamental algebraic mechanics Exponential and Logarithmic Functions Functions and Graphs ISBN-10: 163098132X ISBN-13: 978-1630980207 ISBN-13: 978-1630981235 ISBN-13: 978-1630981327 Linear & Non-linear Systems Polynomial and Rational Functions Polynomial Dynamics: Analyzing higher-degree polynomial equations systems of equations and inequalities Trigonometric Functions Trigonometric Identities and Equations
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