school of mathematics, statistics and applied mathematics...
TRANSCRIPT
Course SummaryMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
December 15, 2020
Introduction to MA161. Numbers Sets Intervals Inequalities Symbols Exercises
Week 1: Introduction; Numbers, Inequalities.MA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
September 28–29, 2020
Functions Examples Vertical Line Test Piecewise Even and Odd Increasing and Decreasing Exercises
Week 2: Functions.MA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
October 5–6, 2020
Catalog Linear Polynomial Power Rational Algebraic Trigonometric Exponential Logarithm Exercises
Week 3: A Visit to the Function Zoo.MA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
October 12–13, 2020
Function Yoga Composition Inverses Exponential Functions. Logarithmic Functions. Inverse Trigonometric Functions. Exercises
Week 4: Composition and LogarithmsMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
October 19–20, 2020
Tangents Limits One-Sided Limits Limit Laws Infinite Limits Exercises
Week 5: Limits and Limit LawsMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
October 27, 2020
Examples Continuity at a Point Continuity on Intervals Limits at Infinity Rational Functions at Infinity Infinite Limits at Infinity Exercises
Week 6: Continuity; Horizontal AsymptotesMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
November 02–03, 2020
Tangents Derivative Rates of Change Derived Functions Higher Derivatives Exercises
Week 7: The DerivativeMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
November 09–10, 2020
Rules Polynomials Exponential Products Quotients Trigonometric Chain Rule Yoga Summary Exercises
Week 8: Differentiation MethodsMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
November 16–17, 2020
Rules Implicit Differentiation Inverse Functions Derived Logarithms Logarithmic Differentiation Indeterminate Forms Exercises
Week 9: Differentiation TechniquesMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
November 23–24, 2020
Extreme Values Critical Points First Derivative Second Derivative Graph Sketching Exercises
Week 10: Graph SketchingMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
November 30–December 1, 2020
Optimization Fence Can Parabola River Semicircle Approximation Antiderivatives Exercises
Week 11: OptimizationMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
December 7–8, 2020
Growth Decay Logistic Pandemic Revision
Week 12: Exponential Growth and DecayMA161/MA1161: Semester 1 Calculus.
Prof. Götz Pfeiffer
School of Mathematics, Statistics and Applied MathematicsNUI Galway
December 15, 2020
• Week 1: Introduction; Numbers, Inequalities. . . where we recall basic concepts which form part of the language of Calculus.Videos: numbers, sets, intervals, inequalities. [Appendix A]
• Week 2: Functions. . . where we explore different ways to represent a function and its properties.Videos: functions, piecewise, even odd. [Section 1.1]
• Week 3: A Visit to the Function Zoo. . . where we compile a catalog of useful functions and their graphs.Videos: linear, polynomial, power, trigonometric. [Section 1.2]
• Week 4: Composition and Logarithms. . . where we use arithmetic and composition to make new functions from old.Videos: yoga, composition, exponential, logarithm. [Sections 1.3–1.5]
• Week 5: Limits and Limit Laws. . . where we introduce limits and laws that help with calculating them.Videos: limits, limit laws. [Sections 2.1–2.3]
• Week 6: Continuity; Horizontal Asymptotes. . . where we study the important concepts of continuity and limits at infinity.Videos: continuity, intermediate, infinity, rational. [Sections 2.5–2.6]
• Week 7: The Derivative. . . where we introduce the derivative as a limit that expresses a rate of change.Videos: derivative, change, derived, higher. [Sections 2.7–2.8]
• Week 8: Differentiation Methods. . . where we list a number of rules that make finding derivatives much easier.Videos: polynomial rule, product rule, trig rule, chain rule. [Sections 3.1–3.4]
• Week 9: Differentiation Techniques. . . where we explore further ways of computing derivatives.Videos: implicit, inverse, log rule, indeterminate. [Sections 3.5–3.6, 4.4]
• Week 10: Graph Sketching. . . where we see how effects of derivatives on graphs are used to sketch them.Videos: extreme, critical, tests, sketching. [Sections 4.1–4.3, 4.5]
• Week 11: Optimization. . . where we apply differentiation to solving a number of optimization tasks.Videos: optimization, parabola, approximation, antiderivative. [4.7–4.9]
• Week 12: Exponential Growth and Decay. . . where we use Calculus to model exponential and non-exponential behaviour.Videos: growth decay, pandemic. [Section 3.8]