Preface
- Page ID
- 4796
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Course Description:
This course provides an introduction to calculus with exposure to applications in science, business, and economics. The main concepts covered are limits, derivatives, and integrals. Derivatives of exponential, logarithmic, trigonometric and inverse trigonometric functions are used to solve optimization, linear approximation, and related rates problems. Techniques of integration and applications are also introduced. Studying calculus will expose students to a variety of important mathematical ideas and help students develop their calculation, critical thinking, and problem-solving skills.
Prerequisite(s): A grade of 60% or higher in Mathematics 30-1 or in MATH 0130, or a grade of C- or higher in any of MATH 1283 or MATH 1285 or equivalent.
The following information gives a quick overview of further learning opportunities at Mount Royal University (MRU) as they relate to this course's scope:
If you are interested in learning more in depth, you can choose to take these courses at MRU: Math 2200 Calculus for Scientists II & Math 3200 Mathematical Methods
Course Learning Outcomes:
Upon successful completion of this course, students will be able to:
- Calculate limits, derivatives, and integrals for a large variety of functions
- Use Calculus concepts in applications
- Communicate solutions clearly in the language of mathematics
A Note on Formatting:
Throughout this resource, practice exercises can be found at the end of each chapter. No answer key is provided, for some of the problems. This is to encourage students to experience mathematics as a synthetic and creative field and also to attend class to ask questions. The "Thinking Out Loud" sections are to prompt discussion - take these up with your classmates and see if you can justify your position using what you know.
Acknowledgments:
The creation of this resource would not have been possible without significant help from a variety of sources. They are, in no particular order,
- Provost's Teaching and Learning Innovation Grant, Mount Royal University
- Professor Delmar Larsen, LibreTexts, for his unconditional support
- The Academic Development Center, Mount Royal University
- The Media Production Group, Mount Royal University
- The Department of Mathematics and Computing, Mount Royal University
- The Faculty of Science & Technology, Mount Royal University
- Former students, who have taken this class in person, and who donated their class notes as reference material, namely, Ms. Merry Faye Graff, Ramandeep Kaur, and Pam Rosete.
- Christopher Gergess, Undergraduate Research Assistant at Mount Royal University
- Rosie Jones, Undergraduate Research Assistant at Mount Royal University
- Jillian Perillat, Undergraduate Research Assistant at Mount Royal University
- Maryanne Thangarajah, University of Waterloo, Undergraduate Research Assistant-Volunteer
- Patrick Thangarajah, University of British Columbia, Undergraduate Research Assistant-Volunteer
Thank you all so very much for your help, insights, and resources.
Pamini Thangarajah, PhD
Calgary, Alberta
September 2018
email: pthangarajah@mtroyal.ca