Introductory Mathematics for Engineering Applications 1st edition by Kuldip Rattan, Nathan Klingbeil ISBN 1118141806 9781118141809

1. STRAIGHT LINES IN ENGINEERING
1.1 Vehicle during Braking
1.2 Voltage-Current Relationship in a Resistive Circuit
1.3 Force-Displacement in a Preloaded Tension Spring
1.4 Further Examples of Lines in Engineering
Problems

2. QUADRATIC EQUATIONS IN ENGINEERING
2.1 A Projectile in a Vertical Plane
2.2 Current in a Lamp
2.3 Equivalent Resistance
2.4 Further Examples of Quadratic Equations in Engineering
Problems

3. TRIGONOMETRY IN ENGINEERING
3.1 Introduction
3.2 One-Link Planar Robot
3.2.1 Kinematics of One-Link Robot
3.2.2 Inverse Kinematics of One-Link Robot
3.3 Two-Link Planar Robot
3.3.1 Direct Kinematics of Two-Link Robot
3.3.2 Inverse Kinematics of Two-Link Robot
3.3.3 Further Examples of Two-Link Planar Robot
3.4 Further Examples of Trigonometry in Engineering
Problems

4. TWO-DIMENSIONAL VECTORS IN ENGINEERING
4.1 Introduction
4.2 Position Vector in Rectangular Form
4.3 Position Vector in Polar Form
4.4 Vector Addition
4.4.1 Examples of Vector Addition in Engineering
Problems

5. COMPLEX NUMBERS IN ENGINEERING
5.1 Introduction
5.2 Position of One-Link Robot as a Complex Number
5.3 Impedance of R, L, and C as a Complex Number
5.3.1 Impedance of a Resistor R
5.3.2 Impedance of an Inductor L
5.3.3 Impedance of a Capacitor C
5.4 Impedance of a Series RLC Circuit
5.5 Impedance of R and L Connected in Parallel
5.6 Armature Current in a DC Motor
5.7 Further Examples of Complex Numbers in Electric Circuits
5.8 Complex Conjugate
Problems

6. SINUSOIDS IN ENGINEERING
6.1 One-Link Planar Robot as a Sinusoid
6.2 Angular Motion of the One-Link Planar Robot
6.2.1 Relations between Frequency and Period
6.3 Phase Angle, Phase Shift, and Time Shift
6.4 General Form of a Sinusoid
6.5 Addition of Sinusoids of the Same Frequency
Problems

7. SYSTEMS OF EQUATIONS IN ENGINEERING
7.1 Introduction
7.2 Solution of a Two-Loop Circuit
7.3 Tension in Cables
7.4 Further Examples of Systems of Equations in Engineering
Problems

8. DERIVATIVES IN ENGINEERING
8.1 Introduction
8.1.1 What Is a Derivative?
8.2 Maxima and Minima
8.3 Applications of Derivatives in Dynamics
8.3.1 Position, Velocity, and Acceleration
8.4 Applications of Derivatives in Electric Circuits
8.4.1 Current and Voltage in an Inductor
8.4.2 Current and Voltage in a Capacitor
8.5 Applications of Derivatives in Strength of Materials
8.5.1 Maximum Stress under Axial Loading
8.6 Further Examples of Derivatives in Engineering
Problems

9. INTEGRALS IN ENGINEERING
9.1 Introduction: The Asphalt Problem
9.2 Concept of Work
9.3 Application of Integrals in Statics
9.3.1 Center of Gravity (Centroid)
9.3.2 Alternate Definition of the Centroid
9.4 Distributed Loads
9.4.1 Hydrostatic Pressure on a Retaining Wall
9.4.2 Distributed Loads on Beams: Statically Equivalent Loading
9.5 Applications of Integrals in Dynamics
9.5.1 Graphical Interpretation
9.6 Applications of Integrals in Electric Circuits
9.6.1 Current, Voltage, and Energy Stored in a Capacitor
9.7 Current and Voltage in an Inductor
9.8 Further Examples of Integrals in Engineering
Problems

10. DIFFERENTIAL EQUATIONS IN ENGINEERING
10.1 Introduction: The Leaking Bucket
10.2 Differential Equations
10.3 Solution of Linear DEQ with Constant Coefficients
10.4 First-Order Differential Equations
10.5 Second-Order Differential Equations
10.5.1 Free Vibration of a Spring-Mass System
10.5.2 Forced Vibration of a Spring-Mass System
10.5.3 Second-Order LC Circuit