Figure 1.1 Representing a weight by a dot or point
Figure 1.2 Abstracting a cantilever beam with a weight
Figure 1.3 Can all of these actions be described using the same mathematics?
Figure 1.4 A black-box diagram of a system
Figure 1.5 Idealizing a phone as a system
Figure 1.6 Simple spring and mass system
Figure 2.1 Rectangular coordinates
Figure 2.2 Screenshot of AutoCAD sketch
Figure 2.3 A 3-D coordinate system
Figure 2.4 Beam supported by cables
Figure 2.5 Finding the end of the beam, E
Figure 2.6 Demonstration of polar coordinates
Figure 2.9 Visualizing the tensile test
Figure 2.10 Acceleration vector A
Figure 2.11 Position vectors pointing out the end points of A
Figure 2.12 Visualizing the scenario
Figure 2.13 Example of a position vector and a force
Figure 2.14 Outlet pipe with force F
Figure 2.15 Graphical interpretation of the cross product
Figure 2.16 Where do I place my coordinate system?
Figure 2.18 Reorientation of the coordinate system
Figure 2.19 A simple pendulum and possible choices for the origin
Figure 2.20 Alternating current
Figure 2.21 Attempting to relate i to the real line
Figure 2.22 Purely real versus purely imaginary
Figure 2.24 Impedances in series
Figure 2.25 Visualizing the radian
Figure 2.26 Angle classifications
Figure 2.27 Example of a truss
Figure 2.28 Complementary and supplementary angles
Figure 2.29 Intersection of two lines
Figure 2.30 Corresponding angles
Figure 2.31 Angle relationships with parallel lines cut by a transversal
Figure 2.32 Constructing the line segment AC
Figure 2.33 Angle sum of a triangle
Figure 2.35 Plot of the angle, θ, versus the length of x for one rotation
Figure 2.36 Plot of the cosine curve on a wider interval
Figure 2.37 Plot of the sine curve
Figure 2.38 The cosine curve scaled for a triangle with a hypotenuse of r
Figure 2.39 Demonstrating the Pythagorean Theorem for trigonometry
Figure 2.40 Triangle used to define the Laws of Sines and Cosines
Figure 2.41 Area of nature preserve from Example 2.23
Figure 3.1 Visualizing a function
Figure 3.2 When f (x) is NOT a function—one input yielding two (or more) different answers
Figure 3.3 Multiple inputs yielding the same output still means f (x) is a function
Figure 3.4 Drawing out the function using arrows
Figure 3.5 Realizing the mapping is not a function
Figure 3.6 Function f with input of 1 gives an output of 0
Figure 3.7 Domain and range of
Figure 3.8 Embedding information into a picture
Figure 3.10 Sliding a metal rod along metal rails in the presence of a magnetic field
Figure 3.11 Intuitive behavior of an inverse function
Figure 3.12 Graphical relationship between f and f–1
Figure 3.13 Graph of f(x) = x2 and its inverse 
Figure 3.14 Demonstration of the horizontal line test
Figure 3.16 Interpolation versus extrapolation
Figure 3.17 Plot of linear fit from Example 3.8
Figure 3.18 Graph of f(x) = x7 + x5 – 1 near the root
Figure 3.19 Noticing the change in sign around the root
Figure 3.20 Table and plot of approximations from the bisection method
Figure 3.21 First three approximations of x*
Figure 3.23 Continuous functions
Figure 3.24 Discontinuous functions
Figure 3.26 Limit approaching 1 from both sides
Figure 3.27 Disagreeing limits
Figure 3.28 The function f(x) = ex and its end behavior
Figure 3.30 The small-angle approximation
Figure 3.31 Comparison of f(x) and g(x)
Figure 4.1 Plot of the car’s distance over 6 s
Figure 4.2 Meaning of velocity, the slope at t = 4
Figure 4.3 Mass and spring system
Figure 4.4 Position function of the mass, f(t) = sin(t)
Figure 4.5 Cantilever beam rigidly attached to a wall
Figure 4.6 Plot of the voltage across the capacitor
Figure 4.7 Fluid flow through a wind turbine
Figure 4.8 Finding minimums and maximums using the derivative
Figure 4.9 Verifying the point at x = 1/3 is a maximum
Figure 4.10 The physical meaning of integration—determining position using velocity
Figure 4.11 Estimating the area under the curve
Figure 4.12 Physical meaning of expected value
Figure 5.1 A more detailed black-box diagram
Figure 5.2 Signal on the screen of an EKG
Figure 5.3 Idealizing EKG as deterministic
Figure 5.5 The signal f(t) = 3sin(5t + π)
Figure 5.7 An everlasting signal
Figure 5.9 An anticausal signal
Figure 5.10 A noncausal signal
Figure 5.11 The signal 
for positive time
Figure 5.15 Integral of an odd function over a symmetric interval
Figure 5.16 Moving a function/signal without changing its shape
Figure 5.17 The function f(t) = t2
Figure 5.18 The shifted functions (original curve is gray and dotted)
Figure 5.19 Delaying f(t) = t2 (original curve is gray and dotted)
Figure 5.20 Scaling f(t) = sin(t) vertically by 3 (original curve is gray and dotted)
Figure 5.21 Scaling f(t) = sin(t) horizontally by 3 (original curve is gray and dotted)
Figure 5.22 A causal signal and its time reversal (original curve is gray and dotted)
Figure 5.23 A causal signal flipped over the x-axis
Figure 5.24 A signal lasting only 4 seconds
Figure 5.25 Intended periodic signal, y(t)
Figure 5.26 The Heaviside Unit Step Function
Figure 5.27 A 12-volt battery and a switch
Figure 5.28 Graphical subtraction
Figure 5.29 The windowed signal, y(t)
Figure 5.30 The impulse function
Figure 5.31 The shifted impulse functions
Figure 5.32 The flipped impulse function
Figure 5.33 The impulse function shifting through the other signal
Figure 5.34 Pairing numbers in the sum from 1 to 100
Figure 5.35 The n versus Sn curve for 
Figure 5.36 The n versus Sn curve for 
Figure 5.37 Eight-term approximation (dotted) of 
Figure 5.38 The standard square wave
Figure 5.39 Adding the first sinusoid
Figure 5.40 Adding the next two terms
Figure 5.41 Using seven terms to approximate the square wave
Figure 5.42 One period of the sine wave with the signum function
