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- https://math.libretexts.org/Courses/Western_Oregon_University/Math_110%3A_Applied_College_Mathematics/00%3A_Front_Matter/01%3A_TitlePageMath 110: Applied College Mathematics for Western Oregon University Copyrighted by Leanne Merrill
- https://math.libretexts.org/Courses/Western_Oregon_University/Math_110%3A_Applied_College_Mathematics/02%3A_Numbers_in_ContextExplore how relationships between numbers shape our everyday life and learn skills to answer common questions involving numbers.
- https://math.libretexts.org/Courses/Western_Oregon_University/Math_110%3A_Applied_College_Mathematics/03%3A_The_Language_of_LinesSee how a common type of relationship between numbers can be used to solve problems and make predictions.
- https://math.libretexts.org/Courses/Western_Oregon_University/Math_110%3A_Applied_College_Mathematics/04%3A_Exploring_Exponential_EquationsEncounter a new type of relationship between numbers and practice using it in real-life situations.
- https://math.libretexts.org/Courses/Mount_Royal_University/Linear_Algebra_with_Applications_(Nicholson)/3%3A_Determinants_and_Diagonalization/3.7%3A_Supplementary_Exercises_for_Chapter_3In general, det[Aij]=det[(Aij)T]=det[(AT)ji] by (a) and induction. Write AT=[a′ij] where \(a^\prime_{ij}...In general, det[Aij]=det[(Aij)T]=det[(AT)ji] by (a) and induction. Write AT=[a′ij] where a′ij=aji, and expand detAT along column 1. detAT=n∑j=1a′j1(−1)j+1det[(AT)j1]=n∑j=1a1j(−1)1+jdet[A1j]=detA
- https://math.libretexts.org/Courses/Mount_Royal_University/Linear_Algebra_with_Applications_(Nicholson)/1%3A_Systems_of_Linear_Equations/1.3%3A_Homogeneous_Equations/1.3E%3A_Homogeneous_Equations\[\mathbf{a}_1 = \left[ −1301 \right], \ \mathbf{a}_2 = \left[ 3120 \right], \mbox{ and } \mathbf{a}_3 = \left[ \begin...a1=[−1301], a2=[3120], and a3=[1111] r[−21000]+s[−20−110]+t[−30−201]
- https://math.libretexts.org/Courses/Mount_Royal_University/Linear_Algebra_with_Applications_(Nicholson)/1%3A_Systems_of_Linear_Equations/1.6%3A_An_Application_to_Chemical_Reactions/1.6E%3A_An_Application_to_Chemical_Reactions_ExercisesCH4+O2→CO2+H2O. NH3+CuO→N2+Cu+H2O. Here NH3 is ammonia, \(\mbox{...CH4+O2→CO2+H2O. NH3+CuO→N2+Cu+H2O. Here NH3 is ammonia, CuO is copper oxide, Cu is copper, and N2 is nitrogen. CO2+H2O→C6H12O6+O2. This is called the photosynthesis reaction—C6H12O6 is glucose.
- https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/1%3A_Power_Series/1.1%3A__Power_Seriesif there exists a real number R>0 such that a power series centered at x=a converges for |x−a|<R and diverges for |x−a|>R, then R is the radius of convergence; if the power series ...if there exists a real number R>0 such that a power series centered at x=a converges for |x−a|<R and diverges for |x−a|>R, then R is the radius of convergence; if the power series only converges at x=a, the radius of convergence is R=0; if the power series converges for all real numbers x, the radius of convergence is R=∞
- https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/2%3A_Ordinary_differential_equations/2.3%3A_Linear_Second_Order_Nonhomogeneous_Linear_Equations/2.3E%3A_ExercisesIf ω is a constant, differentiating a linear combination of cosωx and sinωx with respect to x yields another linear combination of cosωx and \(\sin\omega ...If ω is a constant, differentiating a linear combination of cosωx and sinωx with respect to x yields another linear combination of cosωx and sinωx. has a particular solution that's a linear combination of cosωx and sinωx if and only if the left side of (???) is not of the form a(y″, so that \cos\omega x and \sin\omega x are solutions of the complementary equation.
- https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/5%3A_Vector-Valued_FunctionsHe stated that comets that had appeared in 1531, 1607, and 1682 were actually the same comet and that it would reappear in 1758. Halley’s Comet follows an elliptical path through the solar system, wit...He stated that comets that had appeared in 1531, 1607, and 1682 were actually the same comet and that it would reappear in 1758. Halley’s Comet follows an elliptical path through the solar system, with the Sun appearing at one focus of the ellipse. Kepler’s third law of planetary motion can be used with the calculus of vector-valued functions to find the average distance of Halley’s Comet from the Sun.
- https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Methods/9%3A_Vector_Calculus/9.1%3A_Vector_Fields/9.1E%3A_ExercisesFor the following exercises, let \vecs{F}=x\, \hat{\mathbf i}+y\, \hat{\mathbf j}, \vecs{G}=−y\, \hat{\mathbf i}+x\, \hat{\mathbf j}, and \vecs{H}=−x\, \hat{\mathbf i}+y\, \hat{\mathbf j}. Match ...For the following exercises, let \vecs{F}=x\, \hat{\mathbf i}+y\, \hat{\mathbf j}, \vecs{G}=−y\, \hat{\mathbf i}+x\, \hat{\mathbf j}, and \vecs{H}=−x\, \hat{\mathbf i}+y\, \hat{\mathbf j}. Match the vector fields with their graphs in (I)−(IV).