Introductory Mathematics for Engineering Applications

ISBN-13: 9781119604426 / Angielski / Miękka / 2021 / 464 str.

Craig M. (Wright State University) Baudendistel

Spis treści

Preface viAcknowledgement viii1 Straight Lines In Engineering 11.1 Vehicle during Braking 11.2 Voltage-Current Relationship in a Resistive Circuit 31.3 Force-Displacement in a Preloaded Tension Spring 61.4 Further Examples of Lines in Engineering 7Problems 182 Quadratic Equations In Engineering 312.1 A Projectile in a Vertical Plane 312.2 Current in a Lamp 352.3 Equivalent Resistance 362.4 Further Examples of Quadratic Equations in Engineering 38Problems 503 Trigonometry In Engineering 613.1 Introduction 613.2 One-Link Planar Robot 613.2.1 Kinematics of One-Link Robot 613.2.2 Inverse Kinematics of One-Link Robot 693.3 Two-Link Planar Robot 733.3.1 Direct Kinematics of Two-Link Robot 743.3.2 Inverse Kinematics of Two-Link Robot 763.3.3 Further Examples of Two-Link Planar Robot 813.4 Further Examples of Trigonometry in Engineering 91Problems 994 Two-Dimensional Vectors In Engineering 1074.1 Introduction 1074.2 Position Vector in Rectangular Form 1084.3 Position Vector in Polar Form 1084.4 Vector Addition 1114.4.1 Examples of Vector Addition in Engineering 112Problems 1245 Complex Numbers In Engineering 1345.1 Introduction 1345.2 Position of One-Link Robot as a Complex Number 1355.3 Impedance of R, L, and C as a Complex Number 1365.3.1 Impedance of a Resistor R 1365.3.2 Impedance of an Inductor L 1365.3.3 Impedance of a Capacitor C 1375.4 Impedance of a Series RLC Circuit 1375.5 Impedance of R and L Connected in Parallel 1395.6 Armature Current in a DC Motor 1415.7 Further Examples of Complex Numbers in Electric Circuits 1435.8 Complex Conjugate 148Problems 1496 Sinusoids In Engineering 1606.1 One-Link Planar Robot as a Sinusoid 1606.2 Angular Motion of the One-Link Planar Robot 1636.2.1 Relations between Frequency and Period 1646.3 Phase Angle, Phase Shift, and Time Shift 1656.4 General Form of a Sinusoid 1676.5 Addition of Sinusoids of the Same Frequency 169Problems 1767 Systems of Equations In Engineering 1887.1 Introduction 1887.2 Solution of a Two-Loop Circuit 1887.3 Tension in Cables 1937.4 Further Examples of Systems of Equations in Engineering 196Problems 2108 Derivatives In Engineering 2238.1 Introduction 2238.1.1 What Is a Derivative? 2238.2 Maxima and Minima 2268.3 Applications of Derivatives in Dynamics 2308.3.1 Position, Velocity, and Acceleration 2308.4 Applications of Derivatives in Electric Circuits 2458.4.1 Current and Voltage in an Inductor 2488.4.2 Current and Voltage in a Capacitor 2528.5 Applications of Derivatives in Strength of Materials 2558.5.1 Maximum Stress under Axial Loading 2618.6 Further Examples of Derivatives in Engineering 265Problems 2709 Integrals In Engineering 2829.1 Introduction: The Asphalt Problem 2829.2 Concept of Work 2879.3 Application of Integrals in Statics 2909.3.1 Center of Gravity (Centroid) 2909.3.2 Alternate Definition of the Centroid 2989.4 Distributed Loads 3009.4.1 Hydrostatic Pressure on a Retaining Wall 3019.4.2 Distributed Loads on Beams: Statically Equivalent Loading 3029.5 Applications of Integrals in Dynamics 3079.5.1 Graphical Interpretation 3139.6 Applications of Integrals in Electric Circuits 3199.6.1 Current, Voltage, and Energy Stored in a Capacitor 3199.7 Current and Voltage in an Inductor 3289.8 Further Examples of Integrals in Engineering 333Problems 34210 Differential Equations In Engineering 35410.1 Introduction: The Leaking Bucket 35410.2 Differential Equations 35510.3 Solution of Linear DEQ with Constant Coefficients 35610.4 First-Order Differential Equations 35710.5 Second-Order Differential Equations 38310.5.1 Free Vibration of a Spring-Mass System 38310.5.2 Forced Vibration of a Spring-Mass System 38710.5.3 Second-Order LC Circuit 394Problems 39711 Probability and Statistics In Engineering 40911.1 Introduction 40911.2 Quality Control Probability in Manufacturing 40911.3 Manufacturing Tolerance of Resistors 41211.4 Probability of Accepting/Rejecting Manufactured Resistors 414Problems 420Answers To Selected Problems P-1Index I-1