Calculus for Engineering Technology

Mathematics

Author: Vismar Jay Alfaro
Publisher: University of Science and Technology of Southern Philippines- Jasaan
Source: LibreTexts
License: Mixed
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 157 sections

01: Algebra Review
1.01: Algebraic Simplification
1.02: Factoring
1.03: Quadratic Equations
1.04: Complex Numbers
1.05: Quadratic Equations with Complex Roots
1.06: Multiplying and Dividing Rational Expressions
1.07: Adding and Subtracting Rational Expressions
1.08: Complex Fractions
1.09: Rational Equations
02: Polynomial and Rational Functions
2.01: Representing Intervals
2.02: Solution by Graphing
2.03: Solution of Polynomial Inequalities by Graphing
2.04: Solution of Rational Inequalities by Graphing
2.05: Finding Factors from Roots
2.06: Polynomial Long Division
2.07: Synthetic Division
2.08: Roots and Factorization of Polynomials
03: Exponents and Logarithms
3.01: Exponential and Logistic Applications
3.02: Logarithmic Notation
3.03: Solving Exponential Equations
3.04: Solving Logarithmic Equations
3.05: Applications of the Negative Exponential Function
04: Functions
4.01: Function Notation
4.02: Domain and Range of a Function
4.03: Maximum and Minimum Values
4.04: Transformations
4.05: Toolbox Functions
4.06: Piecewise-defined Functions
4.07: Composite functions
4.08: Inverse Functions
4.09: Optimization
05: Conic Sections - Circle and Parabola
5.01: The Equation of the Circle
5.02: The Equation of the Parabola
5.03: Applications of the Parabola
06: Sequences and Series
6.01: Sequences
6.02: Arithmetic and Geometric Sequences
6.03: Series
6.04: Sum of a Series
07: Combinatorics
7.01: The Fundamental Principle of Counting
7.02: Factorial Notation and Permutations
7.03: Permutations and Combinations
7.04: General Combinatorics Problems
7.05: Distinguishable Permutations
7.06: Probability
08: Right Triangle Trigonometry
8.01: Measuring Angles
8.02: The Trigonometric Ratios
8.03: Solving Triangles
8.04: Applications
8.05: More Applications
09: Graphing the Trigonometric Functions
9.01: Trigonometric Functions of Non-Acute Angles
9.02: Graphing Trigonometric Functions
9.03: The Vertical Shift of a Trigonometric Function
9.04: Phase Shift
9.05: Combining the Transformations
10: Trigonometric Identities and Equations
10.01: Reciprocal and Pythagorean Identities
10.02: Double-Angle Identities
10.03: Trigonometric Equations
10.04: More Trigonometric Equations
11: The Law of Sines and The Law of Cosines
11.01: The Law of Sines
11.02: The Law of Sines - the Ambiguous Case
11.03: The Law of Cosines
11.04: Applications
12: Functions and Graphs
12.01: Prelude to Functions and Graphs
12.02: Review of Functions
12.2E: Exercises for Section 1.1
12.03: Basic Classes of Functions
12.3E: Exercises for Section 1.2
12.04: Trigonometric Functions
12.4E: Exercises for Section 1.3
12.05: Inverse Functions
12.5E: Exercises for Section 1.4
12.06: Exponential and Logarithmic Functions
12.6E: Exercises for Section 1.5
12.R: Chapter 1 Review Exercises
13: Limits
13.01: Prelude to Limits
13.02: A Preview of Calculus
13.2E: Exercises for Section 2.1
13.03: The Limit of a Function
13.3E: Exercises for Section 2.2
13.04: The Limit Laws
13.4E: Exercises for Section 2.3
13.05: Continuity
13.5E: Exercises for Section 2.4
13.06: The Precise Definition of a Limit
13.6E: Exercises for Section 2.5
13.R: Chapter 2 Review Exercises
14: Derivatives
14.01: Prelude to Derivatives
14.02: Defining the Derivative
14.2E: Exercises for Section 3.1
14.03: The Derivative as a Function
14.3E: Exercises for Section 3.2
14.04: Differentiation Rules
14.4E: Exercises for Section 3.3
14.05: Derivatives as Rates of Change
14.5E: Exercises for Section 3.4
14.06: Derivatives of Trigonometric Functions
14.6E: Exercises for Section 3.5
14.07: The Chain Rule
14.7E: Exercises for Section 3.6
14.08: Derivatives of Inverse Functions
14.8E: Exercises for Section 3.7
14.09: Implicit Differentiation
14.9E: Exercises for Section 3.8
14.10: Derivatives of Exponential and Logarithmic Functions
14.10E: Exercises for Section 3.9
14.R: Chapter 3 Review Exercises
15: Applications of Derivatives
15.01: Prelude to Applications of Derivatives
15.02: Related Rates
15.2E: Exercises for Section 4.1
15.03: Linear Approximations and Differentials
15.3E: Exercises for Section 4.2
15.04: Maxima and Minima
15.4E: Exercises for Section 4.3
15.05: The Mean Value Theorem
15.5E: Exercises for Section 4.4
15.06: Derivatives and the Shape of a Graph
15.6E: Exercises for Section 4.5
15.07: Limits at Infinity and Asymptotes
15.7E: Exercises for Section 4.6
15.08: Applied Optimization Problems
15.8E: Exercises for Section 4.7
15.09: LHopitals Rule
15.9E: Exercises for Section 4.8
15.10: Newtons Method
15.10E: Exercises for Section 4.9
15.11: Antiderivatives
15.11E: Exercises for Section 4.10
15.R: Chapter 4 Review Exercises
16: The Derivative
16.01: Prelude to the Derivative
16.02: Limits and Continuity
16.03: The Derivative
16.04: Power and Sum Rules for Derivatives
16.05: Product and Quotient Rules
16.06: Chain Rule
16.07: Second Derivative and Concavity
16.08: Optimization
16.09: Curve Sketching
16.10: Applied Optimization
16.11: Other Applications
16.12: Implicit Differentiation and Related Rates
16.E: The Derivative (Exercises)