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TMATH 124: Calculus I
Concept Study Guide
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Below you can see the list of our 27 objectives for the quarter, divided into six units, each one tied to one or more of the Student Learning Outcomes (SLO) for TMATH 124. For each objective, you will find several links that you can use as a study aid while you're preparing for the unit quiz, including specific pages from the textbook, recommended study problems, interactive graphing demos, and online video lectures (made by both myself and others around the web). Everything I've created specifically for this course is highlighted in purple.

To prepare for any given class day, check the Canvas calendar to see which topics we'll be covering, then watch my video lectures for those topics, read over the examples you find in the textbook, and complete the assigned concept checks on Canvas. (Other resources are entirely optional.) Then you'll be ready to begin work on the homework assignment on WebAssign. (Unless otherwise noted, all page numbers refer to our course text Calculus: Early Transcendental Functions (9th ed.), by Stewart, Clegg, and Watson.)

~Prof. Tou
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Unit A: Functions and Analytic Geometry
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1[Sec. 1.3] Combine functions with composition.Supports SLO #1, 5
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Topic 1 Video Lecture: Composing FunctionsTextbook Reference:
pp. 40-42		Recommended Exercises:
1.3 #33, 39, 43; Diagnostic
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 ⤷ Recommended Video: Functions and Domains [Panopto]——
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 ⤷ Recommended Video: Inequalities and Interval Notation [RP]——
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 ⤷ Underlying Concept: The Domain of a Functionpp. 8-101.1 #39, 41, 47
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 ⤷ Underlying Concept: Set-Builder Notationp. A3—
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2[Sec. 1.5] Find the inverse of a given function.Supports SLO #1
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Topic 2 Video Lecture: Inverse FunctionsTextbook Reference:
pp. 54-58		Recommended Exercises:
1.5 #23, 27, 29, 31; Diagnostic
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 ⤷ Recommended Resource: Graphs of Inverse Functions [Desmos]——
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 ⤷ Recommended Review: Logarithmic Functionspp. 58-611.5 #39, 43, 57
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 ⤷ Recommended Review: Inverse Trigonometric Functionspp. 61-641.5 #69, 71, 77
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 ⤷ Underlying Concept: Solving Two-Variable Equations [Khan Academy]——
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3[Sec. 2.1] Use numerical methods to calculate the slope of the line tangent to a curve at a point.Supports SLO #1, 2, 6
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Topic 3 Video Lecture: The Tangent ProblemTextbook Reference:
pp. 78-81		Recommended Exercises:
2.1 #3, 5; Diagnostic
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 ⤷ Recommended Resource: Tangent Line Slope Calculation Tool [Desmos]——
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 ⤷ Recommended Video: Slope Calculation Example [Khan Academy]——
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 ⤷ Related Skill: Using the Table Feature on a Casio Calculator [YouTube]——
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 ⤷ Related Skill: Using the Table Feature on a TI-84 Calculator [YouTube]——
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 ⤷ Underlying Concept: Slope Formula For a Linepp. A12-A14Appendix B #21, 25, 29, 41
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Note: There's no project for Unit A.
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Unit B: Calculating Limits
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4[Sec. 2.2] Use numerical methods to calculate the limit of a function at a point.Supports SLO #2
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Topic 4 Video Lecture: Calculating Limits NumericallyTextbook Reference:
pp. 83-86		Recommended Exercises:
2.2 #19, 21, 25; Diagnostic
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 ⤷ Recommended Video: Using Numerical Methods to Approximate Limits [YouTube]——
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 ⤷ Related Skill: Using the Table Feature on a Casio Calculator [YouTube]——
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 ⤷ Related Skill: Using the Table Feature on a TI-84 Calculator [YouTube]——
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5[Sec. 2.2] Use graphical methods to calculate one-sided limits.Supports SLO #2
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Topic 5 Video Lecture: Determining Limits From a GraphTextbook Reference:
pp. 86-89		Recommended Exercises:
2.2 #6, 7, 9; Diagnostics (A, B)
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 ⤷ Recommended Resource: Estimating Limit Values From Graphs [Khan Academy]——
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 ⤷ Underlying Concept: Definition of a One-Sided Limitpp. 86-87, 100-1012.2 #1, 2
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6[Sec. 2.3] Use analytic methods to evaluate the limit of a function at a point.Supports SLO #2
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Topic 6 Video Lecture: Three Analytic Techniques for Evaluating LimitsTextbook Reference:
pp. 98-99		Recommended Exercises:
2.3 #13, 17, 23, 25; Diagnostic
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 ⤷ Underlying Concept: Limit Laws and Direct Substitutionpp. 95-972.3 #7, 9
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 ⤷ Underlying Skill: Factoring Quadratic Equations [RP]——
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 ⤷ Recommended Video: Calculating a Limit by Expanding and Simplifying [YouTube]——
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[Sec. 2.5] Use the definition of continuity to identify discontinuities from a function's graph.
Supports SLO #2, 3
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Topic 7 Video Lecture: Continuity and DiscontinuityTextbook Reference:
pp. 115-122		Recommended Exercises:
2.5 #3, 4, 5; Diagnostic
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 ⤷ Recommended Resource: Examples of Discontinuity [Desmos]——
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 ⤷ Underlying Concept: Limits of Functions (Topics 4, 5, 6)——
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 ⤷ Related Concept: The Intermediate Value Theorempp. 122-1232.5 #55, 57
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8[Secs. 2.2, 2.6] Use analytic methods to evaluate limits involving infinity.Supports SLO #2
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Topic 8 Video Lecture: Limits Involving InfinityTextbook Reference:
pp. 89-91, 127-134 		Recommended Exercises:
2.2 #29, 31; 2.6 #17, 21, 25, 27;
Diagnostic
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 ⤷ Recommended Resource: Limits with Infinity [Desmos]——
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 ⤷ Underlying Concept: Reciprocal and Power Functions [Desmos]Also see pp. 27-291.2 #3, 4
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 ⤷ Underlying Concept: Definition of a One-Sided Limitp. 862.2 #1, 2
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 ⤷ Recommended Video: Vertical Asymptotes... How? [YouTube]——
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 ⤷ Recommended Video: Horizontal Asymptotes [YouTube]——
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Unit B Project [Sec. 2.3, 2.6]: Projectile Motion
Supports SLO #2
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Unit C: Fundamentals of the Derivative
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9[Sec. 2.7] Use the definition of the derivative to find the equation of the line tangent to a curve at a point.Supports SLO #2, 4, 6
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Topic 9 Video Lecture: The Definition of the DerivativeTextbook Reference:
pp. 140-146		Recommended Exercises:
2.7 #5, 7, 9, 17; Diagnostic
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 ⤷ Recommended Resource: Tangent Lines and the Derivative [Desmos]——
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 ⤷ Underlying Concepts: Tangent Slope (Topic 3), Analytic Methods for Limits (Topic 6)——
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 ⤷ Underlying Concept: Composition of functions (Topic 1)——
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 ⤷ Underlying Concept: Slope Formula For a Linepp. A12-A14Appendix B #21, 25, 29, 41
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 ⤷ Recommended Video: Finding the Equation of the Tangent Line [YouTube]pp. 140-142—
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10[Sec. 2.8] Differentiate a function using the definition of the derivative.Supports SLO #2, 4, 5
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Topic 10 Video Lecture: The Derivative As a FunctionTextbook Reference:
pp. 153-158		Recommended Exercises:
2.8 #3, 13, 23, 27, 31; Diagnostic
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 ⤷ Recommended Resource: The Graph of the Derivative [Desmos]——
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 ⤷ Recommended Video: Derivatives... What? [YouTube]——
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 ⤷ Underlying Concept: The derivative at a point (Topic 9)——
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 ⤷ Related Concept: Differentiabilitypp. 158-1592.8 #27, 31
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 ⤷ Related Concept: Higher-Order Derivativespp. 159-1612.8 #49, 51
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11[Sec. 3.1] Use basic derivative rules to differentiate sums of power functions.Supports SLO #5
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Topic 11 Video Lecture: Basic Derivative RulesTextbook Reference:
pp. 174-179		Recommended Exercises:
3.1 #5, 11, 15, 19, 23; Diagnostic
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 ⤷ Recommended Video: Basic Derivatives with the Power Rule [YouTube]——
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 ⤷ Underlying Concept: The limit-based definition of the derivative (Topics 9, 10)——
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12[Sec. 3.2] Use the product rule to differentiate functions.Supports SLO #5
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Topic 12 Video Lecture: The Product RuleTextbook Reference:
pp. 185-187		Recommended Exercises:
3.2 #3, 5, 21, 31; Diagnostic
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 ⤷ Recommended Video: The Product Rule for Derivatives [YouTube] ——
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 ⤷ Underlying Concept: The limit-based definition of the derivative (Topics 9, 10)——
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13[Sec. 3.2] Use the quotient rule to differentiate functions.Supports SLO #5
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Topic 13 Video Lecture: The Quotient RuleTextbook Reference:
pp. 187-189		Recommended Exercises:
3.2 #11, 25, 33, 35; Diagnostic
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 ⤷ Recommended Video: Quotient Rule Made Easier [YouTube]——
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 ⤷ Underlying Concept: The limit-based definition of the derivative (Topics 9, 10)——
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14[Sec. 3.4] Use the chain rule to differentiate composite functions.Supports SLO #5
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Topic 14 Video Lecture: The Chain RuleTextbook Reference:
pp. 199-203		Recommended Exercises:
3.4 #1, 9, 15, 23; Diagnostic
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 ⤷ Recommended Resource: The Chain Rule... How? When? [YouTube]——
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 ⤷ Underlying Concept: The limit-based definition of the derivative (Topics 9, 10)——
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 ⤷ Underlying Concept: Composition of functions (Topic 1)——
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Unit C Project [Sec. 4.8]: Newton's Method
Supports SLO #6
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Unit D: Derivative Formulas
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15[Secs. 3.1, 3.4, 3.6] Differentiate exponential and logarithmic functions.Supports SLO #5
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Topic 15 Video Lecture: Derivatives for Exponential and Logarithmic FunctionsTextbook Reference:
pp. 179-181, 204-205, 217-220		Recommended Exercises:
3.4 #15, 26; 3.6 #5, 9, 39; Diagnostic
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 ⤷ Recommended Resource: Derivatives of Exp & Log Functions [Desmos]——
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 ⤷ Recommended Video: A Worked Example Using the Chain Rule [Khan Academy]——
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 ⤷ Related Concept: Logarithmic Differentiationpp. 220-2223.6 #45, 47, 53
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16[Sec. 3.3] Differentiate trigonometric functions.Supports SLO #5
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Topic 16 Video Lecture: Derivatives for Trigonometric FunctionsTextbook Reference:
pp. 191-195		Recommended Exercises:
3.3 #5, 7, 13, 19, 29, 39;
Diagnostics (A, B)
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 ⤷ Recommended Video: Three Basic Derivative Problems [YouTube]——
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 ⤷ Recommended Resource: The Derivative of Sine [Desmos]——
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 ⤷ Underlying Concept: Trigonometric Limitspp. 195-1973.3 #45, 47, 51
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 ⤷ Recommended Table: Derivatives For the Six Main Trigonometric Functionsp. 194—
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17[Sec. 3.5] Use implicit differentiation to find the slope of a line tangent to a curve at a point.Supports SLO #5, 6, 7