APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).
Textbook for Portland Community College Calculus sequence.
MTH 251: Includes limits, continuity, derivatives and some applications of derivatives.
MTH 252: Includes antiderivatives, the definite integral, topics of integration, improper integrals, and applications of differentiation and integration.
MTH 253: Includes infinite sequences and series (including Taylor series), vectors, and geometry of space.
MTH 254: Includes multivariate and vector-valued functions from a graphical, numerical, and symbolic perspective. Applies integration and differentiation of both types of functions to solve real world problems.
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.
Active Calculus: Our Goals
🔗Several fundamental ideas in calculus are more than 2000 years old. As a formal subdiscipline of mathematics, calculus was first introduced and developed in the late 1600s, with key independent contributions from Sir Isaac Newton and Gottfried Wilhelm Leibniz. The subject has been understood rigorously since the work of Augustin Louis Cauchy and Karl Weierstrass in the mid 1800s when the field of modern analysis was developed. As a body of knowledge, calculus has been completely understood for at least 150 years. The discipline is one of our great human intellectual achievements: among many spectacular ideas, calculus models how objects fall under the forces of gravity and wind resistance, explains how to compute areas and volumes of interesting shapes, enables us to work rigorously with infinitely small and infinitely large quantities, and connects the varying rates at which quantities change to the total change in the quantities themselves.
🔗While each author of a calculus textbook certainly offers their own creative perspective on the subject, it is hardly the case that many of the ideas they present are new. Indeed, the mathematics community broadly agrees on what the main ideas of calculus are, as well as their justification and their importance. In the 21st century and the age of the internet, no one should be required to purchase a calculus text to read, to use for a class, or to find a coherent collection of problems to solve. Calculus belongs to humankind, not any individual author or publishing company. Thus, a primary purpose of this work is to present a calculus text that is free. See https://activecalculus.org for links to both the .html and .pdf versions of the text. In addition, instructors who are looking for a calculus text should have the opportunity to download the source files and make modifications that they see fit; thus this text is open-source. See GitHub for the source. Since August 2013, Active Calculus - Single Variable has been endorsed by the American Institute of Mathematics and its Open Textbook Initiative.
🔗In Active Calculus - Single Variable, we actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are generated by students. Where many texts present a general theory followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer plausibility arguments for such results, rarely do we include formal proofs. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand calculus for themselves. This approach is consistent with the scholarly consensus that calls for students to be interactively engaged in class.
🔗Moreover, this approach is consistent with the following goals:
To have students engage in an active, inquiry-driven approach, where learners construct solutions and approaches to ideas, with appropriate support through questions posed, hints, and guidance from the instructor and text.
To build in students intuition for why the main ideas in calculus are natural and true. Often we do this through consideration of the instantaneous position and velocity of a moving object.
To challenge students to acquire deep, personal understanding of calculus through reading the text and completing preview activities on their own, working on activities in small groups in class, and doing substantial exercises outside of class time.
To strengthen students' written and oral communicating skills by having them write about and explain aloud the key ideas of calculus.
Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.
Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.
Intermediate Algebra is the second part of a two-part course in Algebra. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of applications found in most disciplines. Used as a standalone textbook, it offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged.
Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.
Note: this is a 57 MB PDF Document.
This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss
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This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.
Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.
This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.
This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.
Learning and Understanding Mathematical Concepts in the Areas of Water Distribution and Water Treatment. From College of the Canyons.
Table of Contents
Section 1: Unit Dimensional Analysis
Section 2: Geometric Shapes
Section 3: Density and Specific Gravity
Section 4: Chemical Dosage Analysis
Section 5: Weir Overflow Rate
Section 6: Water Treatment Math Detention Time
Section 7: CT Calculations
Section 8: Pressure, Head Loss, and Flow
Section 9: Well Yield, Specific Capacity, and Drawdown
Section 10: Horsepower and Efficiency
Section 11: Per Capita Water Usage
Section 12: Blending and Diluting
Section 13: Scada and the Use of mA
Section 14: Water Utility Management
A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.
The two modules contain lessons on Solving Systems of Equations and Solving Equations. Each module contains days of instruction as well as homework problems. The first module contains a Geogebra assessment and the second includes a Jeopardy game.
CK-12's Texas Instruments Algebra I Student Edition Flexbook allows students to better utilize a graphing calculator in understanding the fundamental concepts of algebra.
CK-12's Texas Instruments Algebra I Teacher's Edition Flexbook allows an Instructor to teach students to better utilize a graphing calculator in understanding the fundamental concepts of algebra.